In almost every game, Bowser the primary antagonist of the series kidnaps her and Mario goes on an epic quest to save her. In earlier games, it is assumed Bowser wants to capture Peach to take over the Mushroom Kingdom, while in later games, it is revealed he actually has a crush on her. However despite her kindness and beauty, Peach is not as defenseless as she appears. She is a playable character in Super Mario RPG: Legend of the Seven Stars, where she has powerful healing abilities and in Super Princess Peach, a role reversal occurs where Bowser kidnaps both Mario and Luigi, and thus Peach goes on a quest to save them actually fighting Bowser as the last boss. In Mario spin-off titles such as the Mario Kart series, the Mario Party series and the Mario Sports series, she is also a playable character and she is partnered with Daisy since Mario Tennis for the Nintendo 64. She is also a supporting character in the Paper Mario series and the Mario & Luigi series, but is playable in Super Paper Mario along with Mario, Luigi and Bowser. Peach also appears in Super Smash Bros. Melee as a playable character along with Bowser, Zelda and Ganondorf and she, Bowser, Zelda and Ganondorf also appeared in Super Smash Bros. Brawl as playable characters again. Peach also appeared in the Mario & Sonic series as a playable character and is part of Team Mario.
Mario obviously cares a lot about Peach as he's willing to rescue her countless times. Although neither character has outwardly expressed their affections for each other, it can be assumed that Peach does in fact love Mario for his bravery and determination. Their presumed love-life has since become the core of many internet jokes, most of which are fairly adult in nature.
In Super Mario Galaxy it is insinuated that Luigi "Jumpman" Mario is Rosalina's father, with Princess Peach having been his mother. StarBomb released a song where Luigi was trying to confess his love to Peach, only to be interrupted by Mario, who is depicted as a sex-pest. Peach ultimately decides she'd rather go out with Toad.
As revealed in the Paper Mario series, Bowser is strongly attracted to Peach. In keeping with the comedic tone of the series, Bowser keeps a diary full of Peach-related material and once confessed his love to a poster of the princess before realising his mistake. Bowser also has a son who once referred to Peach as his mother. The exact details of this have never been fully explored. In most Mario-themed games such as MarioKart and Mario Tennis, Bowser doesn't show his usual hostility, implying that his relationship with the other characters may be more complex than first appearances would have one believe.
In Paper Mario: The Thousand Year Door, Peach is captured by aliens and imprisoned on their ship. There, she meets TEC-XX, the ship's computer. TEC tells Peach that her prescence has caused it to have strange feelings that Peach figures out are romantic in nature. TEC is confused by this, but questions Peach further. Over time, Peach and TEC develop a connection. When the alien commander finds out that TEC has been favoring Peach and neglecting its duties, he demands TEC be shut down. TEC's dying words to Peach are "I love you...". In the epliogue, TEC is rebooted with it's memories intact.