Most have already been covered, but I'll throw in my own recommendations:
(*All of these that I'm suggesting are dubbed with the only exception being Persona 4 The Animation which will be available in dub form later next month*)
Naruto -Yes, yes, people dislike it, but it was my first real anime and it will stay in my favorites list.
Baccano! -1930s era gangster story told from the various perspectives of immortals.
Durarara! -A modern day story about gang wars, mythology, and some really great characters. (Izaya is so baller.)
Death Note -I haven't finished it yet, but from what I've seen so far, it's quite promising. Modern day story about Japan's smartest high schooler finding a mystical notebook that can kill anyone as long as their name is written in it.
K-On! -Cutesy show about High school girls and their adventures in a music club. Very light hearted and funny. And cute. Very cute. I almost died from the cuteness.
Persona 4 The Animation -Highschooler transfers to a school in the boonies and finds out he contains a mystical power of summoning other worldly beings and jumping inside the TV to save other highschoolers.
Gurren Lagann -An anime that's about achieving greatness by doing the fucking impossible. And it does just that. It doesn't take itself very seriously and it can be classified as "explosion porn", but it's still one of the best animes ever conceived.
Black Butler -Little kid had his family killed in a fire. Kid then proceeds to make a deal with a demon to protect him from further harm. The demon protects the child in the role of a fucking amazing butler.
Angel Beats -Dude wakes up and finds out he's dead and fights with other dead people in a world where they must confront a little girl named "Angel". The plot gets better so I won't spoil anything here.