Just to name a few I enjoyed with favorites towards the top:

Hellsing
Elfen Lied
Samurai Champloo
FLCL
Initial D
Fullmetal Alchemist
Wolf's Rain
Cowboy Bebop
.hack

well.. since the DBZ debate has settled, I'll put in my more mature choices..

Outlaw Star
Evangelion
Rurouni Kenshin
Berserk
haven't seen too much, but i'd think i'd be into Naruto

Off the top of my head in no order at all:
Bleach
Monster
Berserk(even though it ain't got no ending!)
Scrapped Princess
Gungrave
Fullmetal Alchemist
Last Exile

Series:
Cowboy Bebop
Trigun
Fullmetal Alchemist
Wolf's Rain
Vandread
Rurouni Kenshin (not necessarily Samurai X)
G Gundam (one of my fav's, but you have to actually endure through to the end to like it)
Gundam Wing
Dragon Ball (not Z, and never watch beyond DB)
YuYu Hakusho (if it's uncut)
Chobits (although it's a bit more girly most of the time, it's still perverted)
FLCL
Naruto (you'll probably only like it if you've ever been a fan of DBZ)
Blue Seed
Those Who Hunt Elves
Hellsing (it's a little brief, but awesome soundtrack)
Witch Hunter Robin (it's good, but very dry)
Big O (it's good, but good luck understanding the ending)

Movies:
Vampire Hunter D
Vampire Hunter D: Bloodlust
Princess Mononoke
Cowboy Bebop: The Movie
Fist of the North Star
Puni Puni Poemy
Colorful
Steamboy

Things to stay away from:
Inu Yasha
DBZ in large portions
DBGT in any portion
Neon Genesis Evangelion: End of Evangelion (most disturbing anime movie I've ever seen, I was depressed for about a week)

That's what I can come up with just looking through my own collection. You really have to find what's right for your own personality. Anime can be really good at getting you out of crappy moods, too. Just grab something funny and pop it in the DVD player. Good times.

I really enjoy Shinichiro Watanabe's projects--these include Macross Plus (which he played a less-than-director role in) and both Cowboy Bebop and Samurai Champloo (directed both).

Very talented artist.

-jkpq45

woot

I saw a buncha animes that I liked on the list and a few I didn't, so I'll just chime in with some that are repeats and some that are new:
Bastard - great 6 episodes
Excell Saga - the creator had a little less crack then whoever made Fooly Cooly
Fullmetal Alchemist
Wolf's Rain
Trigun
Cowboy Bebop
Escaflowne (thought the movie sucked)
Kenshin/Inuyasha and even DBZ have some pluses to them.
There was another anime that was pretty much a drama version of Neon Genesis Evangelion - Rah Xephon. (I thought it ended better).

Ranma 1/2 is definately good for a few laughs once you get into it after a few episodes.

Eh, I'm tired and have class, I'll post more later if I remember stuff, but Puni Puni Poemi was great.

Side question for anyone: Why do they do alot of animes with writing in different random languages? For example, everything in Wolf's Rain thats written on the anime itself is in Russian (there was some point they were looking at a map and all the words were Russian is the best example, but its the entire anime). Some animes just have partial, like on Jupiter scenes in Cowboy Bebop things are written in Russian (might be the wrong planet, but one of the places was I believe).

Yes, but when you experience a soundtrack such as Ghost in the Shell: Standalone Complex where quite a few of the songs (including Inner Universe) are in russian, it will blow you away. Origa is incredibly talented as well.

Shinichiro Watanabe, Yoko Kanno, and Origa need to get together and do something spectacular (like Bebop with some GIST:SAC tones).

Anything with the name Yoko Kanno on it can be expected to have fantastic musical prowess--the audio track will always pump up the artistic value of the anime itself.

-jkpq45

Eh, I don't have the most varied base for my judgement, but I show love to:

Rurouni Kenshin (Especially the movies)
Ninja Scroll
Inuyasha
Samurai Champloo
Reign: The Conqurer
Full Metal Alchemist
Bleach (so far, I'm not too far into the series)
DBZ (in small, small quantities)

Ok, here I go now.

Trigun
Elfen Lied (one of the more depressing endings)
Evangelion (the ending does suck balls, but the rest is good)
Hellsing (it's like Trigun with a horror twist)
Ghost in the Shell (both the movies and SAC)
FLCL
Fullmetal Alchemist

And then for some good old classics.

Ninja Scroll
Vampire Hunter D (and Bloodlust)
Akira (still a wonderful mindfuck)

Forgot to mention Reign, but I haven't seen more then a couple episodes - anyone have it that I can borrow or dl it?

And I rather liked some of the songs I heard from Ghost, though I didn't really like the episodes. But that still doesnt answer any WHYs.

Some of those I've seen, some I haven't. Some I recognise, but my GF quickly gets disgusted with too much fan service.

I liked DBZ (8 years ago), until I saw Naurto. Similar concept with major fights, training and such, but much better story line, better music, and fights actually involve different strategies for different characters. Still in production, but those I've seen introduced to the series watch ~100 episodes in one weekend... its just that good. The current season is a series of fillers until the manga gets ahead, but I've seen the current manga and it still kicks major ass.

Bleach is a much different spin on fighting than Naruto. More focus on body and weapon as one vs. Naruto or DBZ being mostly punch and kick. Also still in production, and it's major focus has been on fights, not character developement.

I recommend staying away from english anime. The anime characters I've seen are rarely above age 20, yet the dub companies don't seem to understand that. Naruto and friends start at age 12, yet the characters sound much older. They also tend to make female leads sound like ditzy cheerleaders. Fansubs are available online or on seek, and required for new shows like Bleach.

One I didn't see mentioned was Noir. The story is kinda generic (similar to Borne Identity), but the music kicks ass.

Vandred was also really cool.

Oh yeah, Noir does kick ass. I completely forgot about it.

That is a situation that has generally been rectified in the past couple of years. Especially on series such as InuYasha, Full Metal Panic, Ground Defence Force Maochan, and others. The days of Sailor Moon quality professional dubs from major companies have passed, and the industry is leaning toward more developed vocal talent.

And I personally enjoy all of the shows listed above, including Sailor Moon. The movies are quite funny in English actually. Nothing beats a fairy shouting "Sailor Moon penetrated the black dream hole!" or the vilin's dying breath being "I couldn't do it because, he threw a rose at me."

series:

Cowboy Bebop
Trigun
FLCL
Naruto
DBZ (just cause it took my anime virginity, as i'm sure it did for most)

movies:

Cowboy Bebop Movie
Ninja Scroll
Princes Mononoke
Akira
Naruto Movie