Plus & Minus is the first one that comes to mind.
If you enter the field with Pokemon that both have either Plus or Minus (so the combination can be Plus/ Plus, Minus/ Minus or Plus/ Minus; this is only in Gen V, in Gen IV you need Plus and Minus for this to work), their special attack will be boosted by 50%.
There's also things like the weather summoning abilities which will activate other weather specific abilities:
Sand Stream activates:
- Sand Rush
- Sand Viel
- Sand Force
Snow Warning activates:
- Ice Body
- Snow Cloak
Drizzle activates:
- Dry Skin
- Hydration
- Rain Dish
- Swift Swim
Drought activates:
- Chlorophyll
- Dry Skin (negative effect)
- Flower Gift
- Leaf Guard
- Solar Power
Forecast will also activate under all of these except under Sand Stream.
There's things like Healer, Friend Guard and Victory Star that activates in double battles, but they won't affect or be affected by the partner Pokemon's ability.
List of Abilities
