My Top 5
1. Great Teacher Onizuka
I laughed and I laughed and I laughed. So many funny jokes. Onizuka's facial expressions are legendary. This anime is amazing, as it offers not only a hilarious story with interesting characters, but it also takes on some serious problems and handles them beautifully. Amazing anime.
2. Steins;Gate
The plot is well written; the characters are unique and amazing; great character development; honestly, it's a very solid anime. The plot starts out slow and somewhat interesting but it goes insane half way through. The story is about time traveling, but don't worry, you will probably be able to understand most of it. I don't recall noticing any plot holes, which is rare in the time travel based story, so that was great too. The characters are probably what made this anime shine more than anything.
3. Cowboy Bebop
I'll be honest in saying that some parts were boring, but the overall it was something really different. It probably made its own genre. The characters are ones that you can never forget. That ending was perfect. ;~;
4. Neon Genesis Evangelion
I had to watch it twice and ask Quickfist for help to understand it completely, but it was worth it. The story isn't what you expect it to be. It's no mecha anime, I'll tell you that for sure lol. I wish that it were better around the second half as the production company went bankrupt and unfortunately that affected the quality of the anime's story somewhat. The original ending was a terrible piece of shit which shouldn't exist, but the movie End of Evangelion gave it possibly one of the best endings I've ever seen. 5. Mushishi
I actually started with the manga and eventually got to the anime. This series is unique; I've never seen anything like it before. Anyone who's into anime/manga should at least watch this once, I doubt that you will regret it.
Honorable mentions: Psycho Pass, FLCL, Shiki, Darker Than Black, The Place Promised in Our Early Days, Zankyou no Terror, and Mononoke.