Browsing my Cousin's PBR Guide, I noticed the abilities section within it. After remembering this thread I thought I'd apply the information from there onto here. Bolded information would be add-ons.
[ABILITY]
Honey Gather
[SHORT DESC]
Adds a chance of finding Honey after each battle.
[LONG DESC]
After each battle, there is a chance that a Pokemon with this ability may find Honey. This chance is relative to the level of the Pokemon
(Higher the level the greater the chance), and can only occur if the Pokemon is not already holding at item.
[ABILITY]
No Guard
[SHORT DESC]
Increases wild encounter rate.
[LONG DESC]
When a Pokemon with this ability is first in the party, wild encounters have a higher chance of occuring
[ABILITY]
Sand Veil
[SHORT DESC]
Decreases wild encounter rate when in a sandstorm.
[LONG DESC]
When a Pokemon with this ability is first in the party, wild encounters have a lower chance of occuring, but only when venturing through an area effected by Sandstorm.
[ABILITY]
Snow Cloak
[SHORT DESC]
Decreases wild encounter rate when in Hail.
[LONG DESC]
When a Pokemon with this ability is first in the party, wild encounters have a lower chance of occuring, but only when venturing through an area effected by Hail.
[ABILITY]
Tinted Lens
[SHORT DESC]
Boosts "Not very effective" moves against opponents
[LONG DESC]
When this Pokémon uses a move that is not very effective on its target, the damage is doubled.
So 1/2x Damage becomes normal damage and 1/4x damage becomes 1/2x
[ABILITY]
Trace
[SHORT DESC]
Copies opponents abilities
[LONG DESC]
Upon switching in, this Pokémon copies the opponent's Ability. Trace cannot copy Multitype,
Trace or Forecast
EDIT: Does anyone have research regarding Focus Punch and Iron Fist? I remember somebody saying that IF doesn't boost FP.
In accordance with the official PBR Guide IF doesn't give a boost to FP