Some suggestions needed for this hopeless nOOb :)

[mchick101]

Thanks to everyone. I'm writing all of them down on my list.

It doesn't take me long to watch through a 50+ episode series so I may be back. I'm thinking I just need to really figure out what I like so when I look at lists of anime titles I don't feel like

[xexyzl]

Watch Perfect Blue if you haven't already. If you liked it, watch Paranoia Agent. (Paranoia Agent is "mainstream" though)

[Kosmit]

[Image link]
Try those.

This. More specifically, Baccano! and Mushishi.

Seconded.

Watch Perfect Blue if you haven't already. If you liked it, watch Paranoia Agent. (Paranoia Agent is "mainstream" though)

That too. Generally if you like psychological/drama/kinda trippy movies try Satoshi Kon's works. Those are Perfect Blue, Millennium Actress, Tokyo Godfathers, Paranoia Agent and Paprika.

If you want to try something different (and I do mean different, both in terms of story and graphic style), check out Massaki Yuuasa's creations: Kemonozume, Kaiba and Mind Game.

[surfsama]

Three more that might be worth looking into are:
Hell Girl, Black Lagoon, and the classic Elfen Lied.

I would say these are popular but not mainstream. Hell Girl is a sad story that I found engaging. Black Lagoon is action. Elfen Lied is...both.

[Knowname]

Baccano!, Mushishi (didn't like it, a little too mystery drama for me) and Clannad are all not licensed in the US yet so you'll have to find it on the web

paranormal

I also suggest Berzerk (slightly mainstream) and NaruTaru for your paranoia. P Agent is excellant too, all three of those are available in English.

cyber-punk and sci-fi

Evangelion (mainstream), Cowboy Bebop (mainstream but you GOTTA see it), Macross Frontier (subbed) or you can get the dubbed Macross, it's VERY old but a classic, just Frontier is basically the same thing (not really) just updated. OR you can try Gundam. Gundam and Macross (Robotech) are like Star Wars and Star Trek respectably. If your a Star Wars fan your more likely to enjoy Gundam and the same with ST and Macross.

scary

Ghost Stories (licensed), Ghost Hound (fansub)

old japan/samurai

Samurai Champloo (mainstream), Afro Samurai

fighting

Ranma (licensed comedy, loooooong but just get the first season you'll be happy xD, very old), Tenshi na Konamaiki (fansub and a personal fave), Tenjo Tenge (licensed), School Rumble (licensed)- not sure if you'd term SR as fighting... but I recomend seeing it

If you just want funny than you want Azumanga Daioh.

Now and Than Here and There is awesome drama, you'll like it... I just couldn't figure out what category to put it into

And the same goes for Kino's Journeys. Just get it.

And remember, you can never read an anime by it's description.

[Ishbalan]

Baccano!, Mushishi (didn't like it, a little too mystery drama for me) and Clannad are all not licensed in the US yet so you'll have to find it on the web.

Those are all licensed. Though Baccano! and Clannad aren't fully released yet.

[Knowname]

oh yeah Baccano just got licensed didn't it?? Mushishi I don't care about though. lol

[Brad]

Here's a few of my very favorites series that haven't already been mentioned:

BECK: Mongolian Chop Squad

Really awesome story about the formation of a rock band. It's a very cool and unique slice-of-life/coming-of-age story centered around the main character, Koyuki. He begins as just a very average, kind of shy kid, and he begins to grow and change after he discovers rock music. It has genuine emotion, great writing, and of course a great soundtrack. I'm still amazed at how few people have actually seen it.

Honey & Clover

This doesn't exactly fit your criteria of what you seem to like, but I really think you should give it a shot. It's very different from your conventional romance series. For one, it's set in an art college. I can't think of too many romance-based shows that aren't set in high school. Two, while some of the characters do follow some long-standing anime archetypes (the young-looking and shy moe girl, the strong but conflicted tsundere girl, etc.), they do so with clever writing, and really fleshed out personalities. You end up (or at least I did) caring for each character and just want to spend more time with them.

NANA

Another kind of drama/romance type show, but the core of this one is about friendship than anything else. Once again, like H&C, the characters are actually older and un-conventional. It also has a lot to do with rock music. It tackles the much more complex side of relationships, involving sex, betrayal, figuring yourself out, all traits that are most often overlooked or simply non-existent in your typical romance/drama show.

I don't really watch a lot of anime anymore, but I've always stuck by these shows. Others that I can mention but I won't go into a long spiel about are:
Cowboy Bebop, Evangelion, REC, Nodame Cantabile, FLCL, Battle Athletes Victory, Fushigi Yuugi, Macross Frontier, Rurouni Kenshin, Visions of Escaflowne, GoldenBoy, and Chrono Crusade.