Pikachu is an Electric-type Pokemon who's first appearance were in the Japanese video games Pokemon Red and Green (1996). His first appearance in the USA was in the similiar games Pokemon Red and Blue (1998). Contrary to popular belief, the Pokemon anime did not air before the games were released. Pokemon Red and Blue came out on September 1st, 1998, while the anime aired 7 days later on September 8th.
Pikachu's National Dex number is #25. He can evolve to Raichu via exposure to a Thunderstone. A baby form of Pikachu named Pichu was introduced in the Game Boy Color sequels to Red and Blue, Pokemon Gold and Silver (2000). Pichu is #172 in the National Dex, and could only be obtained by breeding a Pikachu or Raichu with another compatible Pokemon.
Pikachu's rise to fame stems from the fact the main character of the Pokemon anime, Ash Ketchum, is given a Pikachu by Professor Oak as a starter Pokemon.
In Pokemon Red and Blue, the protagonist Red could also obtain a Pokemon from Professor Oak, although his choice was limited to Bulbasaur, Charmander, and Squirtle (Pokemon which Ash caught during his quest).
The character Ash seems to based on Red in appearance only, as Red was a silent protagonist and didn't have a personality.
Soon after the anime began airing in America, Pikachu became the poster-boy of the Pokemon franchise. Easily the most famous of Pokemon, Pikachu is known by almost everybody in the world and appears on countless Pokemon merchandising.
In fact, Pikachu became so famous that he became a playable character in the Nintendo fighting game Super Smash Bros. (1999) for the Nintendo 64, along with fellow Pokemon Jigglypuff. Appearing alongside such famous Nintendo fighters as Mario, Link, and Samus Aran only helped propel Pikachu to the level of stardom that he now holds. Pikachu was top tier in the game, and was considered by many players to be the most powerful character in competitively play.
In the 2 year gap in between the release of Super Smash Bros. and its sequel, Super Smash Bros. Melee, Pichu also became a fairly popular character. He, alongside Pikachu, Jigglypuff and Mewtwo, became a playable character in Super Smash Bros. Melee.
Pichu was a "clone" of Pikachu (meaning he had the same moveset), but he was much weaker. He was a bottom tier character - in fact, he was at the very bottom of the tier list. Pikachu himself moved down from top tier to low tier.
Pikachu has already been confirmed for the upcoming release, Super Smash Bros. Brawl (February 10, 2008), but most believe that Pichu won't return due to him being a clone of Pikachu and being the worst character in the previous game.
What?! Pikachu is evolving!
Congratulations! Your Pikachu evolved into Raichu!