Just lend a girl something & give her the game manual (if it has one).
Whenever I want to get a girl-pal into gaming, I let them borrow American McGee's Alice; an old PC game, then to spark their interest, I threaten to shave them bald if they don't return it or if the disc is scratched. If Alice isn't their thing, I buy them a cheap copy of Aveyond. If they like Alice, I tell them to go to GameTap & try Serious Sam, if they like Aveyond, I lend them Dungeon Siege. In the end, if neither shooters nor RPGs spark any interest, I default to The Sims or Sim City 3000 Unlimited, RTSs like Heroes of Might & Magic 4 or Age of Empires, & the surefire "Sam & Max." If S&M is the favorite after trying everything else, then I know they were ment to be casual gamers.