Let's see
My favorite is probably Romantic Comedies. It's weird though, because I missed out on a lot of series due to video games, but I still ended up watching some Shounen.
Shounen is probably like my second favorite. I really like a group of friends with strong powers working together to defeat the evil people. Only thing I hate about the Anime is the fillers. Also how you only get 1 episode per week, and if the series is long..it'd take over 5 years to finish the series lol.
I'm a fan of good Mecha/Sci-Fi series. Space Dandy was pretty cool, and funny so I enjoyed that one, but I'm a big big Gundam Fan since I was a kid. Gundam Wing, and Gundam Seed had awesome stories, and Space is one of my favorite things in the universe, so I can't go wrong with that. Still didn't finish TTGL.
I'm not a big fan of Horror genres in Anime because I can't find anything scary or horrifying about them. This is Anime we're talking about. There's a bunch of Cooky characters with weird powers in the Anime Universe, so I can't really get scared. I heard Tokyo Ghoul is good, so I'll watch it.
Psychological like Steins;gate Mirai Nikki was awesome, but I'm not really a big fan of them. Mystery is the same. I like some, and I hate most, but whatever. Then there's the moeblobs. Stuff like K-ON, Lucky Star, A- Channel Mitsudomoe. I enjoyed those too once in a while.
All in all. I used to be a big Anime freak. Seen over 600 different Anime/Movies, and own a lot of anime original sound track. That's what got me into a lot of underground japanese music like hard style/beatmani etc.