From Bulbapedia, the community-driven Pokémon encyclopedia.
From Generation III onwards each Pokémon gained abilities inherent to their species. These abilities have different effects: from helping the Pokémon, lowering the opponent's status, prevent status changes, change the weather, restore HP under certain conditions, transform or even hinder the user, among many more.
A Pokémon specie with only one ability will always have that ability unless Skill Swap is used on it during a battle. A Pokémon specie with two abilities, normally called dual, has a 50%-50% chance of having one or the other, it depends on the internal number generated at the moment of encountering or hatching it. A Dual ability Pokémon will always have the same Ability given by the number generated even when evolving (eg. a Horsea with Swift Swim upon evolution will always change its ability to Poison Point as a Seadra for both being the Ability 1 in that evolutionary family. The same Seadra with Poison Point will always revert into Swift Swim if evolved into a Kingdra. A Horsea with Sniper will always have Sniper no matter what stage of evolution it goes into.)
Some abilities where introduced in Generation IV, changing some Pokémon from Single to Dual ability users. This change, denoted by an asterisk (*), will be reflected upon transferring the Pokémon via Pal Park into a Generation IV game. So even if a Pokémon had an ability when caught in a Generation III game it may or may not be modified depending on the internal number assigned to that Pokémon.
List of Pokémon