Nurse Joy
Nurse Joy (Japanese: ジョーイ Jōi) is (or are) kind nurses who take care of Pokémon. Her Japanese name is a play on 女医 joi, woman doctor.
In the Anime
Nurse Joy is not a single entity. Rather, there are dozens and dozens of Joys working at Pokémon Centers across the regions.
As a rule, Nurse Joys are kind, earnest, honest Pokémon nurses who take care of sick and injured Pokémon.
They are not entirely identical, though aside from themselves, it seems that Brock is the only one who can tell them apart. Nurse Joy has been voiced by 2 people in the Japanese version, 白石文子 Ayako Shiraishi from EP002 to EP229, 山口由里子 Yuriko Yamaguchi from EP245 onwards; and young Nurse Joy is voiced by 雪乃五月 Satsuki Yukino.
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.
There are some notable Nurse Joys that are very different from the others: the muscle-bound kayak-riding Nurse Joy in the Orange Archipelago, for example.
Although there are many exceptions, Nurse Joy will generally have Chansey to assist her. In fact, Chansey's evolution added in Generation II, Blissey, appears physically similar to Nurse Joy. Further driving home the connection, Blissey's Japanese name can be taken to mean "Happy Nurse".
It would seem that the Nurse Joy family is related to the Officer Jenny family.
In addition, Nurse Joys apparently give out Starter Pokémon to trainers in towns or cities without Pokémon Professors.
Pokémon
This listing is for Nurse Joy's usual Pokémon in the anime.
Other
This listing is for Pokémon various individual Nurse Joys have had during the course of the anime.
In the Games
A Nurse Joy and a Chansey operate every Pokémon Center in Pokémon Yellow, but other than that, Chansey does not appear. An old news page from Game Freak on Pokémon Yellow suggests her name is Joy (ジョーイ) the same as in the anime.