There are very few:
- Aerilate, Refrigerate, Pixilate, Normalize - They change the type of moves to usually allow the user to gain STAB. Mega Salamence has Aerilate, which means Normal moves gain STAB.
- Overgrow, Blaze, Torrent - Powers up Grass, Fire, Water moves when "in a pinch'.
- Pickup and Honey Gather - Both allow the user to pick up items, Pickup has random items while HG gathers only Honey.
- Oblivious, Own Tempo - Stop the user from being infatuated or confused respectively.
Edit (Credit to MeepTheMareep02):
Cloud Nine and Air Lock - Negate the effects of weather
Fairy Aura and Dark Aura - Boost the power of Fairy and Dark type moves respectively
Mold Breaker, Turboblaze and Teravolt - Moves ignore the effects of Abilities
Plus and Minus - Boost Sp. Atk when another Pokémon has Plus or Minus
Static, Flame Body, Poison Point, Effect Spore - Contact with the user inflicts a status condition
Gooey - (may be classified as above as it works similarly) - Contact with the user lowers the opponent's Speed
Huge Power and Pure Power - Double the user's Attack stat
Rough Skin and Iron Barbs - Contact with the user inflicts damage
Sand Steam, Drizzle, Drought and Snow Warning - Starts a certain weather when the user enters the field
Primordial Sea, Desolate Land and Delta Stream - (can be classified as above) Same as above, but with harsher weathers
Snow Cloak and Sand Veil - Boosts Evasion in certain weathers
Swarm - Same as Blaze, Overgrow and Torrent
Guts and Quick Feet - Boosts Attack and Speed if the user is afflicted with a status condition
Flare Boost and Toxic Boost: (can be classified as above) Boosts a certain stat when afflicted with a certain status condition
Filter and Solid Rock - Reduces damage from super effective attacks
Volt Absorb and Water Absorb - Electric and Water-type moves restore HP
Competitive and Defiant - Raises a certain stat when another is lowered
Hope I helped!