Death Note is good, but it is more of a psychological thriller than an action show (but it's so good you might like it anyway, lol).
Naruto, imo, is also good, and certainly something to watch if you like action.
Bleach has some of the best choreographed fight scenes in an anime, and it's also very well drawn.
Full Metal Alchemist has quite a bit of action in it, but if you don't like heavy drama, then you might consider avoiding it.
D.Gray-Man, again, has some nice action scenes, but be warned that it can also be pretty dark at times (not as dark as Death Note, but still).
Soul Eater is a great new show that started a little bit ago. It has plenty of action and hilarious random comedy moments.
Samurai Seven is probably the perfect show if you like samurai action (well, that and Samurai Champloo).
These are all I can think of off of the top of my head.