Adaptation: The user changes type depending on the environment. Probably won't suit any existing Pokemon.
Grassland: Grass
Forest: Bug
Sea: Water
Cave: Rock
Mountain: Fighting
Rough Terrain: Ground
Urban: Poison
There could be other areas such as the chargestone cave which could make the user electric type, or grave sites that make the Pokemon ghost type.
Disaster: Summons an unfortunate event at the end of every turn. This would be so overpowered for Absol!
It may Summon: Sunny Day, Rain Dance, Hail, Thunder, Earthquake, Hurricane, Blizzard, etc.
Eh, Absol does not summon disasters, he predicts them.
Anyway, here are a few of mine:
Dimension Twist:
Automatic Trick Room when the Pokemon enters the battle.
Serrated Rust:
Steel-types only. When hit by a Water-type attack, the Pokemon's speed will drop by 1 stage but its attack and special attack will raise by two stages.
Copycat:
If the opponent has one of its moves the same as your, then your Pokemon's move will have doubled the power.
Extrapolation:
Super effective moves on your Pokemon will do x4 damage (x8 if double weakness), while NVE moves will only do x1/4 damage (x1/8 if double resist)
Delayed Nerves:
The Pokemon will only receive damage from an attack the turn after the move. Cannot switch until all damage has been received.
Last Stand:
Once the Pokemon has only 1 HP left, it's attacks will be boosted by x8. If the Pokemon has more than 1 HP, then it's attack will be halved.
Tactician:
All attacks are buffed by x2 power, albeit the second usage of the attack will have it's power at x1, then the third use at x0.5 and so on. The counter will reset if the attack is switched.
Fragile Speedster:
Can use two moves in a turn, but the Pokemon will receive x3 damage per attack.
General's Morale:
When in a double or triple battle, all of the Pokemon on the ability user's side(except the one with the ability) will have all its stats up by two stages. Once the Pokemon with the ability faints, the boost will be gone and the Pokemon will have all it's stats returned to normal and then dropped by two stages.
Defensive Stance:
At the end of every turn, the Pokemon's attack and special attack will drop by a stage, but its defense and special defense will increase by two stages.
Absent:
Moves such as Fly, Dive, Dig, and Bounce will have their power doubled.
Gambler's Luck:
If the Pokemon's current HP's has 2 or more digits and they all match (such as 11,22,111,222), then its moves will all be critical hits.
Determination:
The Pokemon will not lose speed when paralyzed, or attack when burned.
Extremity:
Allows your Pokemon to burn Fire-types, freeze Ice-types, and poison Poison-types and Steel-types.
Just a few that I've just thought.