I don't enjoy a particular genre, I'm pretty picky when it comes to anime. I usually pick shows whose synopses look interesting to me, and I watch them to see if they're any good.
I'm not a huge fan of overused cliches and tropes. It's also really easy for a given character to start annoying me (i.e. hyperfeminine girls, whiny/indecisive/unassertive boys, etc), so a lot of anime I've watched have fallen by the wayside.
Lolis are an easy way to get me to watch a show, but they can also just as easily completely ruin one for me.
If I had to pick a genre that I'd say I'm most on the lookout for, probably Adventure, but that's super vague.