Although many video games seem geared toward boys, girls love playing them, too. Take a Saturday afternoon and fire up your console for a battle to the virtual death.
With some guidance from you, let your daughter pick the type of game she'd like to play. Whether it's a dance, music-based or even a fantasy game, let her explore worlds she might find interesting. Just be sure to pay attention to the rating and make sure it's appropriate for her age.
Also prepare to be schooled -- it's quite likely your daughter may be a much better gamer than you are, but that's a good thing. Allowing her to teach you the finer points of play will help her build confidence.