if you haven't watched these, watch them! lol
FLCL - If you haven't watched this anime yet, it's better that you do. The entire series is 6 episodes long and it's one of those special anime where the anime is actually better than the manga. And nice psychological/sci-fi/comedy/romance anime. It has one of the best anime soundtracks, too. A personal favorite of mine. =D
Fullmetal Alchemist - I recommend this if you're bored watching DBZ or whatever because I have to agree that this is one of those anime that will be remembered decades from now. Really nice character development and awesome plot. Though after Episode 25, it starts to slightly go downhill, but it's still awesome. Only 51 episodes long. Once you watch a single episode, you will just get sucked in and it will never let you go. If you dislike how the anime ends, read the manga. You'll be a lot satisfied with it. The manga is still going, by the way. I actually watchied this anime before it was even released here in the US... so... yeah... one of my personal favorites.
Azumanga Daioh - Cute and totally hillarious. Very...um...unique characters. You'll eventually fall in love with all the characters of the show even though there's no straight plot into it. Just watch it if you really need a laugh. The cabin episodes are the best. ;D
Cromartie High School - Like Azumanga, but a lot more random and instead of girls, it's guys. Watch it if you're a fan of Queen... or Robots that think they're human. Or gorillas. Very funny and very random. Each episode is less than 15 minutes long.
LastExile - Watch it if you want a serious anime or you love the blend of 2D animation and CGI. If you're a person who likes anime with a great plot, watch this one. Really suspenseful though it moves quite slow towards the middle. But nice and satisfying finish. Awesome intro. One of my personal favorites.