From Bulbapedia, the community-driven Pokémon encyclopedia.
From Generation III onwards each Pokémon gained Abilities inherent to their species. These Abilities have a variety of different effects: helping the Pokémon, lowering the opponent's status, prevent status changes, changing the weather, restoring HP under certain conditions, transforming, or even hindering the user, among many more.
A Pokémon species with only one Ability will always have that Ability unless it is temporarily changed during a battle, by a means such as Skill Swap. A Pokémon species with two Abilities has a 50% chance of having one or the other, depending on its personality value. A dual-Ability species will, due to the retention of the personality value as the Pokémon evolves, keep the first Ability or second Ability of its species on evolution, even if the Abilities are different for different stages. For example, a Horsea with Swift Swim will always have Poison Point if evolved into Seadra, as Swift Swim is Horsea's first Ability, and Poison Point is Seadra's. If evolved further into Kingdra, the Seadra's Ability will return to Swift Swim, as this is Kingdra's first Ability. A Horsea with Sniper, however, will retain this Ability throughout its evolutionary line, as this is the second Ability of Horsea, Seadra, and Kingdra.
Some Abilities introduced in Generation IV were assigned to Pokémon introduced in the previous generations, changing them from being single-Ability Pokémon into dual-Ability Pokémon. When transferred through Pal Park, a Pokémon will keep its Generation III Ability, however, upon evolution, the Ability may change into the other Ability for the species, depending on the personality value of the Pokémon. In this way, a Horsea with Swift Swim caught in Hoenn could become a Seadra with Sniper, but only if Horsea's personality value dictated it.
Most Pokémon were given Hidden Abilities in Generation V, with several Abilities introduced in Generation III and Generation IV, as well as in Generation V, now being assigned legitimately to Pokémon of all five generations. In this way, some Pokémon now have the ability to have any of three Abilities—two dependent on their personality value if caught normally, and one for Pokémon obtained in certain ways, such as from the Pokémon Global Link.
List of Pokémon
Generation I families
Generation II families
Generation III families
Generation IV families
Generation V families
Generation VI families
Generation VII families
Generation VIII families