The first game of the series, simply named Pokémon Stadium was released in Japan in 1998. This version featured only around 50 Pokémon, not the full 151 Pokémon featured in the original Gameboy versions. This version was also not released outside of Japan.
The second game in the series was called Pokémon Stadium 2 in Japan and simply as Pokémon Stadium in North America. It was released in Japan in 1999 and in the North America in 2000. This version did feature all 151 original Pokémon featured in the original Gameboy games. The North American version of this game featured support for Pokémon Red, Blue, and Yellow.
The third game in the series was called Pokémon Stadium 3 in Japan and in North America, Pokémon Stadium 2. This version was released in Japan in late 2000 and in North America in mid 2001. This version also saw a European release in late 2001. This game featured support for all third original Gameboy games, plus the three Gameboy Color games, Pokémon Silver, Gold, and Crystal. It featured all the 251 Pokémon, including the 100 brand new Pokémon introduced in Pokémon Silver, Gold, and Crystal.
A fourth game in the series is not being released on the Nintendo 64 but instead on the Nintendo Gamecube under the name Pokémon Colosseum. This title has already been released in Japan in the year 2003 and is expected to be released in North America in March of 2004. This title features support for Pokémon Ruby and Sapphire and is expected to not have support for the first six titles on the Gameboy and Gameboy Color platforms. However, this title will feature all 386 Pokémon within it’s data and is expected to support the upcoming Pokémon games, Pokémon Fire Red and Leaf Green.
Not entirely related, but another Pokémon video game on the Gamecube takes over some of the duties featured in the earlier Pokémon Stadium games. This game, Pokémon Box, allows players to store their Pokémon from Pokémon Ruby and Sapphire on a Gamecube memory card. This game was released in Japan on May 30th, 2003 and while expected to be released, a North American release date has yet to announced.