Worthwhile Units

Worthwhile Units by Base Summoning Rarity
This is a quick list of units you should seriously consider trying in your adventuring party, and/or leveling up if you win them from a summon. It is not at all complete, so please don't assume that just because a unit isn't on this list, that means it isn't as good. The maximum star rating a unit can achieve through ranking up is listed after the entry. (6-star is the highest possible ranking, and 5-star is the highest possible base rarity.)

2-Star base rarity
The first three story/main character units in the game start out at the 2-star rarity level. Of these three, Rain is the one who's worth leveling up the most. By the time he reaches 6-star status, he has some very useful skills and can serve a number of roles. He never outclasses most other 6-star characters, but he's no slouch.

3-Star base rarity (blue crystal)

 * TImothy is a wood sprite with low stats, but a monstrous skill set centered around crippling your enemies with powerful debuffs. Some players still rely on him to run debuffs even on highly difficult end-game content, because his skills are so good. (5*)
 * Edgar is the King of Figaro from FF6. His special ability "Chainsaw" is one of the easiest abilities to use when creating a hit chain to multiply the damage of subsequent hits. This strategy, however, requires at least 2 Edgar units, so don't bother with him unless you have 2 or more. (4*)
 * Shantotto is a black mage with a remarkably advanced skillset for a 5-star max unit. She isn't very durable, but two maxed-out Shantottos can quad-cast the rare spell Tornado, creating an enormous elemental chain attack that you can cap with a strong single-hit attack for massive damage. Again, don't bother with her until you have at least 2 copies. (5*)
 * Firion is a strong physical attack unit that gets a whole bunch of special passive abilities that allow him to do vastly increased damage to many specific types of enemies. He starts slow, but can eventually become a pretty formidable chain-capper/damage dealer. (6*)
 * Cloud of Darkness is a hybrid damage-dealing and support unit that can fill a lot of different roles for your party in a pinch. She really comes into her own at the 6-star level, when she gets 30% resistance to all elements and 50% resistance to all status ailments. She also does a lot of extra damage to Human-type enemies, one of the more common boss types. (6*)
 * Charlotte is a tank unit, specialized in mitigating damage to the rest of your party. She's not as durable as most other tanks, but she is only one of two tanks that can be acquired as a 3-star summon. She's no slouch, though - she gets a lot of useful and uncommon skills as she ranks and levels up, and can serve as a perfectly viable tank for pretty much all of the main story content. (6*)
 * Exdeath is an oddity - a black magic user who wears heavy armor. This enhances his durability somewhat, but it also badly hampers his equipment selection in the late game, when maximizing core stats becomes a much more important priority. Nevertheless, his strong spells and high durability can make him a very useful black magic caster for most of the main story, or until you get someone better. (6*)
 * Cecil is the other tank unit that's available at the 3-star summon level. His skill set isn't quite as effective at pure tanking as Charlotte's, but his powerful healing and support skills make him a bit more flexible. Charlotte is slightly preferred in the current late-game meta-environment, but Cecil set the bar for tanks for a long time, and he's still very good. (6*)
 * Bartz, the protagonist of FFV, is a well-rounded unit with some unusual skills that allow him to perform in a support role while still offering decent damage output and high survivability. His main draw is his ability to restore MP for the party, but he's got a grab bag of skills for any situation. (6*)
 * Ruggles is a decent physical attack unit that can also debuff Earth resistance on your enemies, and serve as a mana battery (restoring MP to the party) in a pinch. He only reaches a 5-star maximum, so he's not as useful in the late game, but he's still a good, solid unit that will serve you well for a long time if you use him. (5*)
 * Kefka is an extremely powerful black mage who's hampered by his lack of the Dual Black Magic skill, a must-have for late-game content. Nevertheless, his strong magical abilities and unique passive trait that drastically boosts magic damage he deals to Human-type enemies makes him situationally useful from time to time, even in the endgame. (6*)
 * Garland is a powerful physical attack unit that does extra damage to Humans. He is somewhat hampered in the meta-environment because he prefers to wield a single weapon rather than dual-wield, which ends up hurting his damage output. He can serve as a formidable damage dealer for most story content, though. (6*)
 * Cerius is a support unit who specializes in elemental protection. He isn't always useful, but when you're up against a boss whose attacks all share an element, his support can make the difference between a tough fight and a laughably easy one. His main problem is that he has nothing else to do except provide elemental buffs; get in a fight where those don't matter, and he's useless. (6*)
 * Lenna is probably the best healer that's available at the 3-star level. She eventually learns to cast 2 white magic spells per turn, allowing her to heal and cure status ailments at the same time. Until you get a stronger healer at a 4 or 5-star base rarity, she's likely to be your best bet, and she will stay useful for a long time. (5*)
 * Arc is a very useful "all-rounder"-type black mage unit. He has good elemental coverage, the Osmose skill (which lets him drain MP from monsters), and can cast 2 black magic spells per turn. He can serve as your workhorse black mage until you get someone better, and will be sufficient for most of the currently available story content. (5*)
 * Scarmiglione is a surprisingly useful physical damage unit. Although his raw damage output is modest at best, his 5-star rank skill "Gas" damages and inflicts status ailments on all enemies for a modest MP cost, which can turn the tide of almost any fight. Well worth taking the time to level up, at least until you get a more versatile status ailment unit like Setzer or Dark Fina. (5*)
 * Ulrica is an unusual physical damage unit who depends on counterattacks to deal extra damage. She's unfortunately hampered by two things: she has no way to draw attacks onto her, and she has a limited selection of equipment she can use. Nevertheless, you may find it worthwhile to find a status ailment-inducing weapon for her and build up her HP so she can counterattack multiple times in a turn and inflict your enemies with free status ailments. (5*)
 * Iris is an odd healing and support unit who uses abilities (rather than white magic spells) to help the party. She gets some healing, including a 30% chance to heal the party whenever she gets hit, but what makes her really interesting as a 5-star max unit is her ability to use the rare skill "Embolden," which powerfully buffs the party's attack and defense, and her ability to inflict the Confuse status on an enemy with "Moogle Attack." She's not a must-have, but she has a little something for every situation. (5*)

4-Star base rarity (gold crystal)
Most 4-star base units are worth using compared to 3-star base units, so this is just a list of a few of my personal favorites. All of the units listed below have a 6-star maximum. However, there are a few 4-star units that can't yet be awakened to 6 stars (such as Leon and Garnet). They have their uses too, but generally won't be as viable as their 6-star-max friends. Most 4-star base units can be awakened to 6 stars.
 * Rikku is a solid support unit who can be used to build chains, quickly escape battles, and even revive your entire party all at once. Given one turn to use her Synthesis ability, she can unlock even more powerful abilities that grant party-wide damage mitigation, set-value damage (damage that ignores defenses completely and always inflicts a set amount), and more. But the real star of the show is her limit break, which casts a 3-turn auto-revive effect on your entire party. Gear her around getting limit breaks fast and you'll be basically indestructible. She also has a great Trust Master Reward (TMR).
 * Ashe is a powerful damage-dealing unit who is also a highly viable chainer. She can inflict physical or magical damage, granting her flexibility against any type of boss, and she has powerful attacks that can simultaneously debuff all enemies' defense and spirit, or heal and/or cure status ailments for the entire party, allowing her to pull double duty without slowing down her damage output. Gear her with magic damage in mind and she'll have the MP to keep using her amazing support-skill attacks alongside her powerful lightning spells. Her TMR is considered one of the better ones in the game.
 * Mystea is, so far, the only unit in the game who's capable of taking magic damage in place of your entire party. She's essentially a magic damage tank, and because there's nobody else like her, she's extremely useful right now. In addition to being able to take the brunt of a full-party targeting magic spell like Ultima or Firaga, Mystea has a repertoire of powerful self-buffs and party buffs to increase everyone's survivability. She's indispensable against any boss that primarily attacks with non-physical moves.
 * Warrior of Light is widely considered the best tank in the game right now. What Mystea does for magic damage, WoL does for physical damage - he buffs his own defense to absurd levels, stands in front of the party, and takes all physical hits for every party member all at once. Combined with powerful debuffs, the Raise skill (to revive a KO'd unit), and a counterattack that heals his HP and MP, there's nothing to dislike about this beastly defensive unit except for the fact that his best abilities don't appear until you max him out at six-star rarity. Put in the work, and you won't be disappointed.
 * Veritas of the Earth is extremely similar to Warrior of Light, described above. His support skills are a little bit different, but his damage mitigation for the party is slightly higher, thanks to the fact that his limit break casts a 3-turn party-wide damage mitigation buff just in case his "stand in front and take damage for everybody" ability doesn't proc right away. He's basically just as good as the Warrior of Light; only WoL's Raise spell, wider equipment selection, and powerful debuffs give him a slight advantage in the metagame. The Earth Veritas is still 100% viable all the way through the endgame.
 * Luka is a healer with some secondary water-damage spells. She has abilities that can be enhanced in the late game with enough gil, allowing her to heal and cure status ailments for the entire party at once. Luka is expensive to make viable, because her abilities really need to be enhanced to make her worthwhile, but she can do a great job as your main healer if you take the time and spend the gil. (A similar unit is Aria, who doesn't need to be enhanced, but whose raw healing abilities are slightly weaker. Aria has the advantage of being able to restore MP to the party, and fully revive the whole party at once.)
 * Cagnazzo is a "provoke tank." Up until now, we've mostly looked at "cover tanks," who cover damage for other characters; a provoke tank attempts to taunt the enemy into attacking only them. Provoke tanks aren't as useful overall because they can't provoke away an attack that's going to hit everyone at once, but they tend to have even better defensive stats and abilities than cover tanks, otherwise. They often also come with valuable secondary buff and support skills. Cagnazzo is the toughest and best-equipped of the 4-star base provoke tanks.
 * Amelia is a high-output physical damage unit with a Jack-of-all-trades grab bag of useful skills for turning the tables on your enemies. She naturally dual-wields guns, so there's no need to outfit her with the Dual Wield TMR. She can also inflict the Stop status on your enemies; Stop freezes them in place for several turns, and unlike its sister ailment Paralysis, it cannot be removed by normal means. She can buff the party, debuff all enemies, and even cast some healing spells in a pinch. If you don't know what lies ahead. Amelia can provide the compact versatility you'll need to survive just about anything.
 * 9S is another versatile support unit, similar to Rikku. 9S's skills are a bit tighter, as they don't need a turn to be activated, but a bit weaker overall in exchange. He can mitigate damage, inflict status ailments, and debuff just about everything, making him an optimal choice for any difficult fight. 9S's TMR is widely considered the most important equipment TMR in the game right now, due to its high versatility.
 * Soleil is one of the few viable dance-based units in the game right now. Dance skills generate a powerful effect, but require the dancer to take no other actions while they're active. Soleil's monstrous party-wide stat buffs (up to a 120% increase on any core stat) are what make the trade-off worth it, but to achieve those powerful effects, you'll need to spend a few million gil enhancing her 6-star abilities. Not especially useful during regular progression, but if you get one, save her and take another look when you reach the endgame and have gil to spare.
 * Zyrus is a powerful black mage who specializes in longer fights and has innate skills that increase his damage against Dragon-type enemies, which can sometimes be very useful. Some of his skills can only be unlocked when certain conditions are met, but he has enough firepower to handle most regular story content right out of the gate. He has special skills that allow him to end up dealing huge damage after a turn or two with the right setup. Zyrus can serve as your primary black mage all the way into the end game, but be sure to practice with him so you can get used to how his strongest skills unlock and interact with each other.
 * Victoria is the other good option for a 4-star base rarity black mage. She's got limited elemental coverage, specializing in dualcasting Dark and Fire-element spells, but she also has a non-elemental spell (Meteor), and some strong support skills. Her most interesting ability is a Dark-element damage dealing skill called Overflow, which "stacks" up to 7 times as it's cast on subsequent turns, adding an additional 120% damage modifier with each stack. In a protracted fight, casting Overflow every turn for 4 or 5 turns will begin to produce obscene amounts of damage per hit. (In a pinch, the fire spell FIraja has a similar effect, and unlike Overflow, it can be cast twice per turn to build stacks fast; however, Overflow eventually results in greater damage.)
 * Chizuru is a samurai who excels at dealing physical damage. She was once considered the most powerful attacker in the game, but that time has long since passed. Nevertheless, her damage output is significant (when she's properly equipped), and two Chizurus can also build chains with each other very easily. In the late game, with ability enhancements and the right equipment, it's possible to give her a 100% chance to dodge physical attacks, allowing you to cheese your way through many bosses and even some optional endgame content by hammering away and never getting hit.
 * Refia is another 4-star option for a healer/white mage. Refia's skills are great, and her stats are solid; unfortunately, she can't dualcast spells, and unlike Luka, she has no combination skills that cover multiple effects (such as healing and status recovery) at once. However, she is a viable healing option for most Season 1 content, and is certainly cheaper to use right out of the box than Luka. Refia was my personal white mage choice for a long time.
 * Xon is a unique unit with a few skills you won't find anywhere else. His archetype is "thief," and he has great skills to that effect, including the ability to steal items from all enemies at once. He also gets some interesting "trade-off" abilities that let him do extra damage in exchange for a self-debuff, such as decreased defense or a higher chance to be targeted by enemies; in addition, he has a complementary skill that allows him to hide from battle for a random number of turns (1-3), and come back with all his debuffs wiped clean. However, the real reason to use Xon is the "Twist of Fate" skill, which copies all positive effects on an enemy, casts them on your party instead, and then dispels them from the enemy. This can make a huge difference in many of the game's toughest battles.
 * Setzer is another unique unit who specializes in building chains and capping them with massive doses of unmitigated damage - if you're lucky. His skillset is built around the idea of gambling; using cards from a magic deck, he deals chain damage to one or all enemies, inflicts status ailments, and more. However, his flashiest skill is the "Double Dice" ability. Double Dice does a set amount of damage to all enemies, with the amount chosen at random from a table of 5 possibilities. Even though its base damage will be a set amount, Double Dice's damage can be modified by chains or enemy weaknesses, which means that rolling the high value on a lucky Double Dice throw at the right time during a long chain can result in millions of unavoidable damage dealt in a single turn. It's always a gamble, but that's the point.
 * Veritas of the Waters is a hybrid magic damage and healing unit with a lot of powerful skills. Unfortunately, her dualcasting ability is hidden behind another skill, meaning you have to waste the first turn setting her up for her to be as useful as possible. Nevertheless, her strong skillset, good base stats, and flexibility in combat make her a great choice for a secondary healer or water-based black mage. In a pinch, she'll make a fine primary healer too, at least until you get someone a bit more specialized.

5-Star base rarity (rainbow crystal)
Every 5-star base rarity unit is worth keeping and leveling up. There's not a single one that isn't useful in some way. However, some 5-star units are generally considered better than others; if you end up with 2 or 3 5-star units that seem to fill a similar role (such as "physical damage"), you might consider doing some research on Google or the "real" Exvius WIki to get an idea of which one to focus on first.