Well, it all depends on how much she's interested in anime. Now, it's possible that the only anime she watches is the stuff that appears on Cartoon Network. Or she may got out of her way for the non-mainstream stuff, as well as dress up as her favorite caharacters and attend an anime convention.
But there are soooooo many genres within anime it's self, that you 2 may or may not like the same ones. There's your romantic comedy animes like Love Hina, His and Her's Circumstances, and Saikano. Your giant robot actions animes, Neon Genisis Evangalion, Gundam, and The Big O. Your action animes, Cowboy Bebop, Trigun, Witch Hunter Robin. And your ultra popular one's like Dragon Ball, Pokemon, Yu-Gi-Oh, and Naruto. And then there's your hentai (anime porno) with intergalatic demons who've come for our women
And let's not forget the anime section in your big bookstores like Borders and such filled with graphic novels. A ton of animes started out this way, and later got an animated series for the fans.
So ask her to take you to her bedroom and have her show you her favorite ones