I like spy movies and post-apocalyptic themes. I don't seek them out, it just seems when I really like a movie it has one of those themes. Sci Fi is pretty great sometimes, too.
Gosh this is hard to say one particular favorite... I think Fantasy & Sci Fi mostly. I have watched every single Star Trek movie countless times and I can't even begin to tell you how many hundreds of times I have seen the Harry Potter series. Recently I watched Ender's Game and quite enjoyed it.
I can watch a good action or comedy but it has to be REALLY good otherwise, I just can't get into it.
Other genres I guess like FhiCat said, specifically military I can enjoy (Blackhawk Down, Saving Private Ryan, etc.)
But I do also enjoy documentary-ish films, "based on a true story" type things like, Schindler's List or The Shawshank Redemption.
I don't consider myself a big movie person. I like older musicals (White Christmas is my all time favorite movie!), some romantic/ romantic comedies (think Ever After, Sweet Home Alabama) or dramas as long as they are on the family friendly side. I've been meaning to watch Mona Lisa Smile one of these days. I have a few animated favorites too. Once I watch with or without my kids.
I tend to like the heavy dramas with a social message. That's probably why I don't watch a lot of movies, even though they are my preference there is a limit to how much I can watch.