I don't like anime that's too stupid with too much pointless humour getting in the way of the story (if there even is one). And I also don't like "fan service" ie. pointless boob/panty flashing, what's the point? It's distracting from the story and the characters and it makes me annoyed. >
For me, there has to be a good story, decent character development, etc. And if it's condensed into around 20-30 action-packed episodes that's perfect. I can't stand stuff that drags on with loads of stupid filler episodes.
Basically the anime I really like is something along the lines of Vision of Escaflowne (my favourite anime of all time, it's just stunning)
I will watch most genres as long as they don't have the above things in them.