I don't really watch a lot of anime, not because I don't want to, but because I just don't have the time or anything. Otherwise, I have a backlog of anime I still plan to watch when I do get the chance. But the few shows I have seen, I've enjoyed them all, so I don't have one that I hate. I guess the one I like the least, which I still absolutely love, was the second half of Death Note, or probably the first story arc of Higurashi no Naku Koro ni (namely Onikakushi-hen, or the 'Demon Killing Chapter').
As for my favourite, definitely Umineko no Naku Koro ni, or 'When the Seagulls Cry'. A spiritual successor to Higurashi no Naku Koro ni (When the Cicadas Cry), most people say it's pretty bad purely because it omits a lot of the stuff that's important in the game plot that it's based on, but as an anime I think it works really well, and I'm desperately hoping for a new series to explain those missing bits and carry the cliffhangers on. Not to mention, I'm a massive fan of chess motifs and of locked room mysteries and supernatural mystery tales...