She first appeared in Super Mario Brothers. In this and subsequent games, she is constantly being kidnapped by King Bowser Koopa, despite the good fighting abilities she demonstrates in Super Mario Bros 2 and Super Mario RPG. In Paper Mario, she sneaks around the castle gathering information to help Mario in his quest.
The Princess rules her kingdom in a giant castle with a multitude of Toad servants. It's unclear as to whether or not there is a King of the Mushroom Kingdom, as the nation's title would suggest. Some video game manuals and Mario comic books refer to a King, but such a character has never appeared in any of the games.
Peach has recently appeared in the Mario Party series, Super Smash Bros. Melee where she demonstrated fine fighting ability in the tournament: she's the strongest and sexiest character in the game (Roy can prove it)... later she went on a much needed vacation to Dolphic (Delfino) Island in Super Mario Sunshine sporting a new dress and having her hair tied up in a ponytail. Unfortunately she is kidnapped yet again, with Mario having to do another rescue mission finally leading to a great vacation.
In Japan, the Princess' name has always been "Peach", it was changed to "Toadstool" when Super Mario Brothers was released in America. Her Japanese and American names were combined into her current title, "Princess Peach Toadstool" when Super Mario 64 was released in the United States.