Wow there are a lot of anime fans here, and I thought it was a music forum
Some of my favorite series:
Trigun - It's got a great story line, pretty deep if you ask me.
Berserk - Just freaking awesome, so much blood and gore, awesome fight scenes.
Dragon Ball Z - okay, flame me now, but I love Dragon Ball Z, GT, and just plain old DB. I like the fights, though I do hate how 2/3 of the episodes were them standing talking. Long series, but it's great.
Serial Experiments: Lain - Crazy awesome story about the internet(or something I'm not entirely sure) I watched about 8 episdoes once when I stayed at my friends place, it's an awesome story, pretty hard to follow, though it might have just been becuase it was 9 in the morning after staying up all night and me falling asleep every 5 minutes(lol) I'd highly recommend it though.
Evangelion - It's an alright anime, my friend is addicted to it, but I'm not the biggest fan of mechs and the such. Still a pretty interesting story line to it.
Love Hina - Another one of my favorites, awesome love story about a guy in college that lives with a bunch of storys(sorry if that's wrong, it's been a good year since I watched it last) Good story line if you like the sappy romance type.
Ai Yori Aoishi - Right up there with Love Hina, pretty much the same deal, I'd say I like this one better than Love Hina though.
Samuri Champloo - Awesome anime about a couple travelling samurai that are followed by a woman looking for her father(I think) Good fight scenes, pretty decent story, and personally I think it had one of the best endings of any anime I've watched. Most leave me with a sense that they aren't finished, but this one pretty much closes it up.
.hack// - An anime about an online video game that is putting people in to comas, it follows a charcter that is stuck in the game and can't log out. It's an odd plot to it, but it's good. I love the soundtrack too, highly recommended.
Cowboy Bebop - Not my favorite, but I'd say watch it just becuase it's a classic. About some travelling bountry hunters and their lives. Deep story line that you have to watch a few times to grasp it all.
Naruto - Again, it's pretty good, but not my favorite. It's quite long, so it's hard to get in to it with out a ton of free time to watch them. I think I watched the first 150 or so episodes of it, it's okay, story line gets old after awhile, repetative, but it gets good around the testing times. I'd say watch it if it's on tv, otherwise don't bother looking for them all and watching them all unless you really like ninja's and idiot main characters.
I'm sure there are tons of other anime that I've watched and forgotten about, but these are the main ones in my mine. I looked through the first 5 or 6 pages of the thread and I'm downloading Honey and Clover, and Elfen Lied, so I'll see how those are.