In battle
Air Lock / Cloud Nine (negates weather)
Battle Armor / Shell Armor (cannot be struck by critical hit)
Clear Body / White Smoke / Full Metal Body (stats cannot be lowered)
Dazzling / Queenly Majesty (immune to priority moves)
Filter / Solid Rock / Prism Armor (super effective damage dealt to Pokemon with these Abilities is lowered)
Soundproof / Cacophony (immunity to sound-based moves)
Gooey / Tangling Hair (lowers opponent's Speed on contact)
Huge Power / Pure Power (doubles Attack)
Insomnia / Vital Spirit (prevents the Sleep status condition)
Minus / Plus (boosts Special Attack if ally has Plus or Minus),
Mold Breaker / Teravolt / Turboblaze (allows moves to hit through opposing Abilities)
Multiscale / Shadow Shield (lowers damage taken when at full HP)
Propeller Tail / Stalwart (ignores things that draw in moves)
Protean / Libero (changes type to move it's using)
Receiver / Power of Alchemy (when ally faints, copies Ability)
Rough Skin / Iron Barbs (inflicts damage on contact)
Wimp Out / Emergency Exit (when at half health, switches out)
Power Construct / Shields Down / Zen Mode (changes form at 50% or less HP)
Out of battle
Flame Body / Magma Armor / Steam Engine (Eggs hatch faster)
Intimidate / Keen Eye (decreases chance of finding Pokemon at a lower level)
Pickup / Honey Gather (finds certain items after battle)
I didn't include some of the examples listed in my source, as I felt they were too different from each other.
Source