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Weapon Skills: Each skill in this section provides special attacks and bonuses when using the relevant weapon types
Swords
Axes
Maces
Staves
Archery
Thrown Weapons
Unarmed Combat

Vanilla Skills: These were released in the original game.
Dual Wielding: This skill is required to use a weapon in each hand, otherwise you suffer severe combat penalties.
Shield Bearer: Special abilities and attacks while using shields.
Berserker Rage: Attacking or being attacked increases attack power! RAAAAR!
Artful Dodger: Helps you to avoid attacks more easily.
Master of Arms: Makes armor, especially heavy armor, more effective.
Vampirism: You lose the ability to regenerate life naturally, and cannot eat food. However, you gain life every time you attack an enemy. You also sparkle in sunlight.
Golemancy: Allows you to create golems, from living silverware to walking mustaches.
Fleshsmithing: Grants a bunch of meat-related abilities, including a literal meatshield.
Mathemagic: You know how they say that math is needed in every job? This is the ultimate result.
Psionics: Mental powers.
Necronomiconomics: Dark magic, but such spells usually come at a cost...
Viking Wizardry: Lots of cold-and-lightning-based magic. Hail Odin!
Astrology: Gain power over the stars and planets.
Promethean Magic: For the pyromaniac in you.
Magic Training: Support skill that makes magic and mana use more effective.
Blood Mage: You regain extra mana by killing things. Also comes with a weakness to light magic.
Ley Walker: Boosts mana regen.
Perception: Helps you hit things and see traps better.
Burglary: Helps you steal stuff.
Assassination: Moar critical hits!
Fungal Arts: This is a weird one. Allows you to grow mushrooms and use them in battle.
Alchemy: Increases your ability to make potions and poisons.
Wand Lore: Wands are more effective and can last longer.
Archaeology: Helps you get rid of traps and create powerful artifacts. You also start with a fedora.
Smithing: Increases your ability to make weapons and armor. Also makes you stronger.
Tinkering: Let's you create traps and other useful devices out of rubbish.

These skills were added with the expansion pack Realm of the Diggle Gods
Big Game Hunter: Grants combat bonuses to animals and earns more meat and experience.
Emomancy: Use the power of eyeliner to deal existential damage.
Werediggle Curse: You can turn into a werediggle for more power! Sadly, in were-form you cannot use other abilities.
Veganism: Animals are less inclined to attack you, and plant-based enemies drop food! However, attacking animals or eating non-vegan food gives harsh penalties. Not really compatible with Big Game Hunter, but there's nothing stopping you from taking both.
Piracy: Extra loot and dirty tricks, yarrr!
Demonology: Grants all sorts of bonuses against demons...provided you can resist the greater power that they offer.

These skills were added in the free expansion pack, You Have to Name the Expansion Pack
Clockwork Knight: Grants all sorts of mechanical attacks, including rocket jumps. Tinkering boosts the effectiveness of mechanical attacks.
Rogue Scientist: For the evil genius in you. Tinkering, Alchemy, and Wand Lore all increase the power of these abilities.
Battle Geology: Become an Earthbender!
Warlockery: For mages who prefer to get up close and personal with foes. Boosts survivability.

Finally, all skills in this section are from mods. They are not guaranteed to get along or scale well with vanilla skills
QiGong: Become a super chi-using fighter!
Bushido: Quintessential samurai skills.
Kung Fu: Provides access to a wide variety of stances. Slightly buggy.
Poisoneer: Gains access to some very nasty debuffs.
Silver Tongue: Wanna talk your way out of problems? This is pretty much the only way to do it.
Ninjitsu: For sneaky, tricky bastards.
Wild Magic: Pretty much mana diarrhea. Can be helpful or hurtful.
Archmage: Difficult and advanced magic. Involves Elder Gods or something.
Degree in Dungeoneering: You go to college in between turns. Little bit of everything, but focused on magic.
Clutch of Midas: Your body slowly turns to gold. You are tougher and richer, but get much slower.
Inquisitor: Divine powers and protection.
Spellsword: Grants magical bonuses to melee combat.
Meteorology: The magic of weather prediction!
Avenging Executioner: For all you serial-killer types. You know who you are.
Galactic Hitchhiker: You're a hoopy frood who knows where his towel is.
Brofistery: You are a bro. Even if you are a woman.
Barrier Maiden: You summon wards and wear skimpy clothing. Even if you are a man.
Radiant Wizard: You unleash pure arcane abilities, at tremendous cost to your own body.
Dastardly Scoundrel: John McLane? Indiana Jones? Posers.

1...2...3...KICK IT! (Drop That Beat Like an Ugly Baby)
AaaaaaAAAAaaaaAAAAA!!! For the Awesome
Amnesia: The Dark Descent
Audiosurf
Bit.Trip Beat
Cogs
Defense Grid: The Awakening
Killing Floor
RUSH
Super Meat Boy
The Ball
The Wonderful End of the World
Toki Tori

Dungeons of Dredmore. It requires you to make a character, die on the first floor, make a second character with the exact same skills, and die on the first floor again. Thankfully, the third time got much further before dieing halfway through a monster zoo.