>Adrenaline
Holds back some effects of status ailments. Eg.: Burns don't lower Attack, Poison drops less HP per turn, Confusion hits for less damage.
For fighting types, I guess?
>Affinity
Gradually receives less damage from consecutive moves of the same type. Eg.: first move hits for 100%, second by 75%, third by 50%, ...
(What would be a good cap for damage reduction?)
I'd say give it to the Eeveelutions as an alt ability.
>Awareness
This Pokémon is immune to the effects of psychological warfare, eg.: Entice, Taunt, Torment, Intimidate ability, etc.
>Free Range
In triples / rotation, this Pokémon's moves can hit any target.
(Could probably function with later gen battling models as well)
>Purveyor
Automatically passes his held item to the ally when the ally loses its own item (even by theft / knock off).
>Siren's Chant
Any "voice" moves can also cause Infatuation.
>Stronghold
If this Pokémon is sent out after all its allies have fainted, its max HP increases by 50%.
Lore-wise, this could be perfect for Starters, since their other normal abilities activate "in the red".
>Targeting
If this Pokémon attacks after its target, it will ignore the target's evasion bonuses, including effects from weather.
Pokémon like Yanma or Venonat could have this one.