Code Geass (Beat the big empire with a cool superpower and lots of strategy)
Death Note (Psychological thriller deal)
Black Lagoon (Old fashioned action, japanese businessman turned pirate in the thailand gulf)
One Piece (Never ending with over 500 episodes, but alot of really good fights and likeable characters. Takes a while to get used to the art style though.)
Full Metal Alchemist Brotherhood (Remake of the original with a tigher more to the point story)
Claymore (Fighter anime with an almost full female cast)
Ofcourse you also have:
Naruto and Bleach, but these are sort of an aquired taste. Some like it alot, others hate it.