The ones I recommend and more or less from best to not-as-good that some people may have mentioned already are:

1. One Piece - read the manga too, it is the best. The first arc or so might bore you, but later on it really starts to get extremely, extremely interesting, fun and imaginative.

2. Soul Eater - Animation, especially fight scenes are really nice and overall has a nice feel to it.

3. Gantz - A lot of gore but overall fun. I prefer the manga though.

4. Rahxephon - If you like Evangelion you'll probably like Rahxephon especially with the 'singing' which I fell in love with.

5. Naruto/Bleach/D.Gray-Man/Katekyo Hitman-Reborn! - Pretty much all lumped together since they are quite similar and more or less quite popular. Once again I prefer reading the manga.

6. A lot more...though not in any particular order; Death Note, Full Metal Alchemist, Full Metal Panic, Azumangah Daioh (hilarious comedy), Ouran High School Host Club (comedy and romance), Lucky Star, Gintama, Welcome to the NHK, Chaos Head (quite similar to Welcome to the NHK based on hikikomori's), Kurenai (similar to Lucky Star in terms of genre). There's lots of great Anime out there.

Oh, and don't watch Hellsing. Watch Hellsing Ultimate. The original Hellsing's ending deviates from the manga and to me was utterly disgusting and lame.