It really depends what you're into, but here are some I really like...
Fullmetal Alchemist: Brotherhood - Just an amazing series. It's a must see for...well, just about everyone.
FLCL - This one's a little wacky and it's kind of hard to get into, but it' only 6 episodes so it's definitely worth a shot. It's a coming of age story told through symbolism involving bass guitars, baseball bats, eyebrows and tv headed robots.
Anohana - This one's really new, the 5th episode just came out today, but it's already getting a lot of buzz. Just a fair bit of warning, it's bound to make you so nostalgic you'll melt into a puddle, but the writing and animation is absolutely incredible.
I would personally avoid the big 3 (Naruto, Bleach, One Piece) simply because there are so many episodes you're bound to get bored somewhere in the middle. Some people swear One Piece is incredible, and you may agree, but I would suggest watching some shorter series before you even try climbing that mountain.