I would mention to you my all-time favourite and some of my favourites for some genre...
All time favourite:
Full Metal Alchemist (The old one and the new-brotherhood)
- Both series share deep story with a vast fantasy world, engaging characters, lots of laughs, lots of tears, lots of drama, and lots of "I am young so friends are important" stuff. If you are into shounen stuff and don't want long anime like Bleach, this is a good choice. Full Metal Alchemist Brotherhood is currently the highest rated anime on the wensite myanimelist.com (something like that)
Romance + Comedy
1. Lovely Complex -> Winner hands down. Combines romance & Comedy perfectly. Win Toradora by 1000x. This is one of the most underdiscovered gem imho. xD
2. Toradora -> Used to be my favourite, but now no more. xD
1. School Rumble 1 -> Pure comedy gag, brainless storyline but likable, and lots of tear-inducing scenes.
2. Seto no Hanayome -> My favourite comedy that I have watched last year. This is just too funny. xD
1. Sora no Otoshimono -> Harem comedy at its best. Simply amusing. Both seasons are nice.
1. Higurashi -> Highly acclaimed and sought after, but I haven't managed to finish it (due to exam hiatus) sigh xD Not motivated to finish this atm.
2. Ghost Hunt -> Anime describing various professions (Priest, Monk, Spirit Medium, Scientist, Maiden) working together to cleanse haunted places/legends and catch ghost ! xD
1. Ouran High School Host Club -> Best school comedy + romance in my opinion. Don't let the art put you off, the comedy is just xD xD xD
2. Kaichou wa maid-sama
1. B Gata H Kei -> A story about a middle school girl trying desperately to get laid in order to become more womanly, and the man that she targets is one ordinary, plain, uninteresting male classmate. Lots of laugh stuff...
1. Kiss x Sis -> This is plain O.O
Actually I do watch TOO MUCH anime, I have infinite list going on... These are the ones that I could remember.
P.S. : Oh ya, for some extra stuff
1. Gantz - horror
2. Liar Game - Japanese drama, nice stuff