Mmm, I do like video games that have anime or manga themes. I have Fullmetal Alchemist and the Broken Angel, which is good, and some with anime- or manga-style graphics like Tales of Legendia (the cut scenes) and cel-shaded like Samurai Legend Mushashi and Shining Force EXA.
What do I like about them . . . ? Well, story is big with me, and they have pretty good stories (FMA, Tales and Shining Force are excellant, Musashi is okay but fun). I love the look of them and the way they play, especially the fights. I guess I just like games, and if they look like anime then all the better.