Officer Jenny
Officer Jenny (Japanese: ジュンサー Junsā) is (or are) police officers who use Pokémon in their duties. Her Japanese name is a play on 巡査 junsa, police; policeman.
In the Anime
Officer Jenny is not a single entity. Rather, there are dozens and dozens of Jennies working as police officers across the regions.
As a rule, Officer Jennies are brave, determined, but ineffective police officers who fight against the likes of Team Rocket, Team Magma, and Team Aqua - along with miscellaneous other criminals.
They are not entirely identical, though aside from themselves, it seems that Brock is the only one who can tell them apart. However, each Jenny will have a different symbol on her hat that indicates location. There seem to be two Viridian Jennies, as during the Indigo Conference, two Jennies with the same hat symbol were seen side-by-side. (We know that the symbol in question--a star--indicates Viridian due to previous episodes.)
Supposedly, they are all extremely similar-looking relatives - cousins, sisters, etc. However, fans have proposed various other theories has been suggested for the strange phenomenon - everything from time travel to cloning. However, they are all voiced by 西村ちなみ Chinami Nishimura in the Japanese version and by Raquel Marinho in the Brazilian dub.
Although there are many exceptions, Officer Jenny will generally have Growlithe to use as a police dog.
It would seem that the Officer Jenny family is related to the Nurse Joy family.
Ash's Squirtle was given to an Officer Jenny who fights fires. It is the leader of a group of four other Squirtles known as the "Squirtle Squad", who serve as the local firefighting team.
Pokémon
This listing is for Officer Jenny's usual Pokémon in the anime.
Other
This listing is for Pokémon various individual Office Jennies have had during the course of the anime.
In the Games
In Pokémon Yellow, Officer Jenny will give out a Squirtle in Vermilion City.