Nice, fresh anime.

[krissy]

xxxHolic is a wonderful show I gotta be honest. And I'm not big on CLAMP in any way ever.

I second Gankatsuou.
Blood+
Gintama.
Ergo Proxy

as far as fresh ones go

[Evolavas]

I'd also recommend RahXephon, its really worth checking out. Others are....

Outlaw Star
Lupin III ( be careful with its movies, some are great, like the Castle of Cagliostro, and some are atrocious, like Legend of the Gold of Babylon )
Tokyo Godfathers
Ghost In The Shell
Kodocha
Maison Ikkoku
Elfen Lied

Eureka 7, Samurai Champloo, Haibane Renmei, and Witch Hunter Robin.

I've seen some of Eureka 7 and Samurai Champloo, but everything else here seems pretty new to me. These titles all seem worthwhile, I'm going to have to check them out as well.

___________
xxxholic
I second Gankatsuou.
Blood+
Gintama.
Ergo Proxy

Added as well, this might take awhile.

[Nominus Experse]

Serial Experiments Lain
Berserk
Vampire Hunter D: Bloodlust

[NINJA_Ryu]

Dont foget Fate Stay Night, Cowboy Bebop, and a good oldie, Ranma :P

[Walshy.indeed]

Hmmm.....

Evangelion
Macross Plus
Tekkaman Blade

Anyone got any old school ones?

[JKTrix]

Ok, I might as well just list my top anime (that I've seen all the way) that are absolutely outstanding.

RahXephon, Gankutsuou, Twelve Kingdoms, Eureka 7, Planetes.

Eureka 7 happens to contain some of my favourite moments in any anime...ever. The emotions linked to the song 'GET IT BY YOUR HANDS' are incredible. It's constantly on my iPod playlist.

RahXephon is just my favourite anime. Eureka 7 (and Fullmetal Alchemist, and Wolf's Rain) were made by the same people who made RahXephon. The people who made RahXephon came from some of the makers of Cowboy Bebop, and most of the staff of Escaflowne. High quality stuff, epic even.

While supernatural abilities/themes are all fine, there's something about a realistic story that nudges it above the rest. Planetes, while it deals with 'currently unreal' commercial space travel, is incredibly realistic with everything that happens being entirely believeable. No superpowered big mechs, no aliens, no hidden magical powers, just people and science. And it is a very good story.

Hajime no Ippo, while older than most of these other shows, is another 'realistic' show. As far as I've seen, no one has any kind of magical power and everything is done by each person's own human abilities.

If a 'realistic' story can be greaty entertaining and engaging, it tends to hold a lot more weight with me. It makes the creator be more creative, being limited to things in 'real life', instead of relying on just making stuff up.

That said, a majority of my favourite anime are supernatural :P R.O.D. features girls with wicked telekinetic origami skillz for cryin' out loud.

[Madame Adequate]

I'd have to recommend Patlabor (I've not seen all the Patlabor stuff, but what I have seen is cool), Kimagure Orange Road, and Ah! My Goddess. For pure fun, completely lighthearted stuff (And also my fave anime ever), go for Azumanga Daioh.

Edit: Yo, Bubblegum Crisis and Moldiver are good too.

[Wolf Kanno]

A lot of the stuff I would recommend has been mentioned so I'm going to list a few older goodies.

Battle Athletes (Preferably the TV series, cause it has the better cast and story) Now I generally don't care for sports anime but this one is hilarious and touching.

Irresponsible Captain Tylor the funniest anime ever! Only show where a captain defeats an entire fleet of aliens just by surrending at the right time

One Pound Gospel, the story of a boxer who falls in love with a nun. It's Rumiko Takakshi but it's more in the vein of Maison Ikkoku than Inu-Yasha or Ranma 1/2

Robot Carnival, it's pretty old and hard to come by but it is gorgeous and entertaining. If you like to see how diverse anime is, this movie is the one to do it. It's a series of animated shorts done by famous directors and writers in Japan arounf the mid 80's. They all share the theme of robots. At times it's funny, action packed, artistic and somtimes just plain beautiful... It's a real hidden gem of an anime.

Captain Herlock: anything with Harlock in the title. In fact, anything by Leiji Matsumoto.

Slayers, cause it's the best damn fantasy anime made. The karaoke scene in season two is alone worth watching this series.

Tenchi Muyo! preferably the OVA and the first movie. Their funny, action packed and surprisingly touching and heart warming. The first movie is gorgeous and has one of the best Tenchi stories.

I'll see if I can remember anymore later.

[Azure Chrysanthemum]

Good call on Patlabor, excellent series.

[NeoCracker]

I don't like the second Patlabor, but the first was amazing. Can't comment on 3.

as for as new ones, theres teh Hellsing Remake, Hellsing Ultimate.

Though the best one to come out recently would be this Ugly yet Beautiful World. Lots of nudity, but not a hentai. Only goes for 12 episdoes, but still awesome.

Lupin III is always a funny one.

Not many people seem to have seen it, but Cosmo Warrior Zero is another worth watching. Same goes For Silent Mobius.

[Madame Adequate]

For some reason, I forgot Fushigi Yugi. >_>;

[Remedy]

Godfathers

I Re-recommend it