Asagi was originally designed for the cancelled game Makai Wars, but she is now used by Nippon Ichi as a mascot/joke character. She is usually seen invading the extra levels of other games attempting to steal the main character position from the game's actual protagonist.
In the "Prinny" series
Prinny: Can I Really Be the Hero? contains a secret unlockable mode in which every boss fight is replaced by a boss fight against Asagi. Over the course of the game, she gradually becomes more and more insane in her attempts to steal the hero role from the prinnies, eventually going so far as to dress in a Prinny suit with a bomb planted in it. Prinny 2 added a game mode called "Asagi Wars" where Asagi (in Prinny form) is the playable character, and every boss fight is against an alternate version of herself.