As mentioned on the main page, there're loads and loads of characters. Here is where data is found on them.
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Shirou Emiya and Servants
Shirou Emiya
Adaptational Badass: He does have over a thousand magic circuits (2,628, to be specific). He also, individually, has the most on-hand Servants. Not to mention the Word Magic...
Jack of All Stats: No Saber has less than a B Rank for any stat. They each "specialize" in one stat or another, but statwise they have no glaring weaknesses.
Lily revealed hers early on, and was thus titled a "Queen".
Alter revealed hers late in life.
Saber/King Arthur (King Of Knights)
Jack of All Stats: Compared to the other three, she's neither the fastest, strongest, toughest, most agile, nor the most powerful, however she's faster than Alter, stronger than Lily, more skilled than Nero, and has the highest magic resistance of the group.
Divergent Character Evolution: The original Saber Alter was just Saber who was corrupted by the Shadow in the Heaven's Feel route. Here, she's given her own distinct history where she went on the warpath on all of Europe.
The Empress: She had conquered all of Europe before her death. Unlike most examples, she was content to leave it there.
My Country, Right or Wrong: Implied - she did what she needed to do for her country, even to the point of staining her sword black with her enemies' blood.
Mighty Glacier: Implied that she's the slowest of the four Sabers, but possesses A-class strength.
The Rival: To Saber, for the wish promised by the Holy Grail.
Tomboy and Girly Girl: She's the most tomboyish of the Sabers, especially when paired with Lily. Her title being "King" despite revealing her gender reflects this - unlike Canon Arturia, she is comfortable with aligning both her gender and her more brusque qualities. She's notThe Lad-ette, however.
Divergent Character Evolution: While not to the degree of Alter, Saber Lily was originally concieved as an alternate Arturia for Fate Unlimited Codes, and gets her own alternate history as described here.
Fragile Speedster: Faster than the other Sabers, incredibly skilled due to having an incredibly long life, and agile, but her strength isn't as high as the others.
The Messiah: Despite difficulty and opposition, she united all of Britain under her leadership and ruled it for many years.
Really 700 Years Old: She lived as an eternally youthful queen for many decades, outliving all of her friends and loved ones, before choosing to pass the crown and Avalon to Mordred so that she can age and die naturally.
Reasonable Authority Figure: For the most part, she is more understanding than Saber is towards Alter's darkened Excalibur. Doesn't mean she didn't want to hurt Alter for making the holy sword black, though.
Tomboy and Girly Girl: Compared to the other Sabers, she's the most feminine, however it really stands out when she's next to Alter.
Who Wants to Live Forever?: She says she grew tired of watching her loved ones die around her, which led to eventually bestowing Avalon to Mordred and aging away gracefully.
The Blacksmith: Her sword, Aestus Estus, was forged by Nero herself in a volcano from the purest ore of the empire, before summoning the greatest spellcasters of the Empire and the known world to enchant it and the high priests of the Olympian Gods to bless it. It's specified that Nero was a masterful smith, as even without the enchantments and blessings the sword was so good that Vulcan possessed his own priest to give Aestus Estus the blessing it deserved.
Lightning Bruiser: Strongest of the four Sabers, A-rank agility, and can copy any Servant's power temporarily, including the other Sabers' Prana Burst ability to increase her abilities.
Panty Shot: As in Fate/Extra, she doesn't even try to draw attention away from the area. Comes with being an...
Attention Whore: Always does her best to get Shirou's attention, through seduction or battle prowess.
Warrior Poet: Nero has a deep appreciation for the arts, unmatched by her peers. This is Truth in Television: Emperor Nero was more of a performer than a ruler.
Blood Knight: Just LOVES a good fight. In fact, that's all he ever wanted in this war. He got one from Samson.
Combat Pragmatist: Saw Shirou's Command Seals and decided eliminating him as soon as possible was the best course of action. Of course, the next thing that happened, ended up breaking the War.
Know When to Fold 'Em: Four Sabers each capable of keeping up with him caused him to retreat. Sure, he might love a good fight, but that was just insane.
The Berserker: Wasp Spasm allows him to nearly match Samson in strength and ability.
Scathach (Caster)
The Ace: Word Of God said that if she got her Temple, she'll be overly broken.
Anything That Moves: One of the first things she does is tell Lancer than she needed to get laid. When Bazett objected, she said Bazett could join in if she wanted to. Bazett ends up waking up between Scathach and Cu Chulainn, naked, after they ravaged her.
Badass Teacher: She taught Cu Chulainn how to use Rune Magic and she can fight him one-on-one and cast rune magic on the fly.
Blade on a Stick: She's the one who gave Lancer Gae Bolg, after all. It's part of her legend as well, plus she can double as a Lancer-class Servant.
Waver Velvet and Servants
Waver Velvet
Iskander (Rider)
Badass Army: His Ionioi Hetairoi, an army of Heroic Spirits who fight for his cause. It is as awesome as it sounds.
Ascended Fanboy: In-Universe. Waver fought alongside him in the Fourth War, therefore he too has become a part of that army.
Genghis Khan (Archer)
A Father to His Men: Claims to have treated his soldiers as if they were his family, why they were/are so loyal to him.
Badass Army: His Noble Phantasm, the Grand Horde. Similar to Iskander's Reality Marble.
Jordan Lionstone and Servants
Jordan Lionstone
Black Sheep: Mostly due to the fact that he's a prodigy in the family, but doesn't go into the research route and instead hunts down Apostles and Sealing Designates as an Enforcer.
Golem: He is accompanied by animated lion statues. Lionstone isn't merely a fancy name, after all.
Demolitions Expert: He's an Enforcer who really knows his way around modern explosives, and applies this knowledge on his jobs.
Resigned to The Call: He didn't even want to join the Holy Grail War, in spite of the Grail choosing him.
The Smart Guy: Knows that Napoleon is supposed to be taller than he is right now, plus he's able to figure out who Assassin is after only hearing her name.
Badass: Not for what he did in battle (though that's still impressive), no, he managed to talk Gilgamesh down and get the King of Heroes to let him live by refusing to simply lie down and die.
Big Eater: While retaining all the manners proper for a court, to boot.
More Dakka: His ranged weapon is all the artillery of the Grande Armée.
The Napoleon: Trope Namer, though not by choice; one of his Noble Phantasms revolves around his shorter-than-history height, and he is most certainly not amused.
Status Buff: His Noble Phantasm Napoleonic Complex, which can be used when facing opponents who are at least ten inches taller than him. It boosts his Strength, Agility, Endurance, and Bravery up a rank. With his 5 foot 2 inches legend-enforced height, he can use it on every other Servant except for the Sabers and Jackie.
Deadpan Snarker: Best summed up when she responds to Luvia's complaint about Herakles being Berserker.
"Oh boo-hoo, someone broke the rules. Get in line. Someone summoned four Sabers. Deal with it."
Parental Substitute: All of her Servants quickly fill the void Kiritsugu left for her and plot vengeance against the rest of Ilya's family when Herakles explains the circumstances surrounding his summoning.
Asskicking Equals Authority: Granted, he's loyal to Ilyasviel and listens to her commands, however, he's not above threatening or nearly killing Ilyasviel's two new servants when they try to fight each other against her orders.
The Berserker: Probably the Ur Example in Mythology, and is noted as a class in which he feels very comfortable in. He is absolutely deadly in upfront combat.
Nigh Invulnerability: Thanks to both his flesh in general, but also to his Nemean Lion armour-pelt, which he can use in a pinch to summon the lion itself.
And since Odysseus had Illya remove Mad Enhancement, he can actually use his brains.
Worf Barrage: Nine Lives should have killed both Lancelot and Sigfried instantly, but they both survived, Lancelot through speed, Sigfried through his own Nigh Invulnerability.
Odysseus (Archer)
Blow You Away: His "Gift of Aeolus" summons torrents of wind.
Improbable Aiming Skills: He is an Archer, after all, and fought in the Trojan War. His Bow of Ithaca NP reflects this, always aiming accurately.
Oh Crap: Has this reaction when he realizes that his new master is quite willing to sic Berserker on him if he doesn't work together.
The Strategist: This is Odysseus we're talking about, here.
Stealth Expert: Can go invisible similar to an Assassin, thanks to his Noble Phantasm "Shroud of Minerva".
Summon Magic: His "The Odyssey" NP allows him to summon anything that he met in his journey, which... is a lot.
Hector (Lancer)
Javelin Thrower: His thrown lances hit as hard as missile strikes, and his Noble Phantasm allows him to turn anything resembling a spear into a low-level Noble Phantasm (like Knight of Honor, except only with spears). It is noted that he fights like an Archer despite being a Lancer.
Blade on a Stick: "Roaring Spear" is his strongest Noble Phantasm, the spear that was only blocked by Ajax's shield. Its power is comparable to an Anti-Army type Phantasm, which surprised Lancelot.
Lightning Bruiser: A-rank speed outside of Mad Enhancement, Strength high enough to rip telephone poles and street signs out from cement and when he turns on the gifts his class grants him, he pushes his abilities even higher. He's fast enough to actually counter the Nine Lives attack from Hercules, which is nine attacks done so fast that they're instantaneous.
Shapeshifting: Can alter his own body at will, which he uses to dodge otherwise lethal arrows.
Siegfried (Rider)
Absurdly Sharp Blade: Gram actually can cut into Hercules. It IS the blade that Caliburn is based off of, after all.
Badass: He can fight Hercules on even terms, folks.
Blood Knight: When he was injured by Hercules, he suddenly grinned and went all out, ignoring all pain and damage done to him during that time.
Nigh Invulnerable: Per his legend, having bathed in the blood of a dragon in order to gain impenetrable skin. Doesn't mean he doesn't feel pain, though: his fight with Hercules left him horribly bruised and beaten.
The Berserker: Can force himself to fight against Herakles evenly, though he admits that Herakles is stronger than he is.
Making a Splash: Doesn't even need to be near water to use this power. Come on, he led a nation through the desert for 40 years and was able to get water to come out of solid rock before he died.
Summon Magic: Snakes, locusts, and The Ark of the Covenant.
Samson (Berserker)
An Axe to Grind: A bronze axe that's made out of the jawbone of a donkey, no less.
Restraining Bolt: The rawhide around his hair keeps it from being destroyed, but it also weakens his strength.
Super Strength: Goes up in proximity to the danger around him.
Medea and Servants
Medea (Caster)
Sugar and Ice Personality: She's pretty aloof and manipulative, but all she wants is to be with her lover.
Sasaki Kojiro (Assassin)
Fragile Speedster/Glass Cannon: He has A+ Agility, but only C Strength and a pitiful E Endurance. His skill makes him a dangerous enemy, but he needs every bit of it to not get hit, because if he does, he's pretty much dead.
Master Swordsman: Stated in canon to be the most skilled fighter in the Fifth War. Able to come out against Lily with minuscule damage through expert swordsmanship and footwork. Of the Servants seen so far, undeniably the most skilled.
Blade on a Stick: Halberd Force, his preferred weapon as a Lancer, as well as a unique form that has four lances attached to each other and can be thrown For Massive Damage.
Boobs of Steel: The bustiest of all females in canon, and probably still larger than even Nero or Scathach in the chest department, she also has A-rank strength.
Super Strength: When Sakura was her master again, her strength went from pitiful C-rank all the way to A-rank, and she can push it further, becoming strong enough that even Nero has trouble matching her.
The Stoic: As per canon, she doesn't show much emotion, though she isn't afraid to speak her mind now that Shinji's dead.
Took a Level in Badass: Compared to his typical summon (canon stats in Fate Apocrypha), Henry rigged the summoning circle to make it seem like he had been summoned in India, granting him more Noble Phantasms and an increase in parameters.
Achilles (Berseker)
Nigh Invulnerable: Achilles is known for this (minus his heel, of course.)
Took a Level in Badass: Compared to a normal summon, he is stronger and has more Noble Phantasms due to technically being summoned in Greece.
