I like Ninja Scroll and Akira, mostly.
If you're going to read instead of watching then I must say DO NOT read Bastard!!
While the first part of the manga is nice, if a bit overexagerated, the second part utterly sucks and makes no sense at all. For reference, watch de anime version. Although incomplete, it actually is pretty good and fun.

I am discovering Stand Alone Complex at the moment, I'm at the 15th episode or something and all I can say is "wow this is really overrated". I discovered the Ghost In The Shell universe with the eponymous movie, which is for me a chef d'oeuvre, and watching this anime after the movie well it looks... flat. The soundtrack Kenji Kawaii produced for the movie is faaaar better than the anime one which is in my opinion not very polished (except for the excellent opening).
I'm disappointed as you can see :(

Eh yeah I'm not that big about anime and manga.
Honestly, the only thing I bother with nowadays is Touhou, and that's usually just the games.
I like watching ghibli stuff with my sisters however. I dunno, but the style in those movies are *just right* for some reason.
Edit: @ op: even if I'm no big one piece fan, that delivering bink's sake song is pretty nice.

Akira and Ghost in the Shell are the blatant demonstration that "cartoon" isn't something that must necessarily mean some pathetic and childish Disney-alike story....
Apart of these two, for made-in-Japan animation really there is plenty of choice. Some names I can recall on the moment:
- Neon Genesis Evangelion
- Full Metal Panic!
- Naruto (Shippuuden)
- Hunter X Hunter
- Nabari
- Michico and Hatchin
- Death Note
- Dragon Ball / Z / GT (R.I.P.)
- Mazinkaiser (the 2000s' Mazinga)
And so on....

Heh if you want to really prove that, try Urotsukidoji

I'm not that much into anime, apart from the absolute masterpieces like Cowboy Bebop or Neon Genesis Evangelion.
On the other hand, I like quite a lot of mangas: One Piece, Shigurui, Berserk, Death Note and so on :)

I'm also a fan of Manga and Anime and Japanese (Pop)culture in general. Sci-Fi is my favored genre but I like fantasy, historical and slice-of-life are also good. I don't like horror, angst or shonen that much.
Anything Ghibli is simply the best and Ghiblis videos are unfortunately the only well made ones available here and only ones with dubs (some of the rest are done so sloppisly that its hard to follow the storyline).
There's not enough variety in manga published in finnish unfortunately either and english ones tend to cost too much (over 10€ per book compared to finnish 6-7,5€ per book). Of the finished series Akira, Azumanga Daioh (have series both in finnish and english), Emma and Gunnm I've liked the most. Best ongoing series are Fullmetal Alchemist, Nausicaä of the Valley of the Wind, Oh! My Goddess and Yotsuba&!.

i'm not too fond of them, especially the mainstream ones (Dragonball, Naruto etc.) but there are some i really like FLCL, Great Teacher Onizuka or Black lagoon; i also like the manga series Berserk and Black lagoon.

@Grog. NGE a masterpiece? If you say so. I personally loathe it. especially Shinji. the biggest whiner ever :)
Cowboy Bepop is indeed one of the best animes out there.
I also love Miyzakis movies. 3 years ago they had miyazaki month on TV which gave me a chance to see his movies for the first time. Simply amazing.

Patlabor was pretty cool, everythings better with big robots
Ninja Scroll was definitely a good watch
Macross Frontier is probably my favourite of the "not turned into Robotech" ones (and possibly of all non-robotech anime), they still had a song repeated far too often but it was a fairly good one and not by that irritating minmei bitch (am I the only one who wished some zentradei would have tripped and crushed her?) Its got a good solid story that actually left me wanting more at the end of each episode which is something no other anime has.
And considering the competition in Anime, thats a pretty damned impressive feat

Big anime fan here.
My biggest favorites are (in no particular order)
-Evangelion
-Lain
-Texhonolize
-Claymore
-Tenjou Tenge
-Elfen Lied
-Ghost Hound
-Paprika
-GiTS (Movies, SAC 1 and 2)
-Ergo Proxy
Well.... easier to check my votes: AniDB

Just to let you guys know, Best Buy is having an anime sale in select stores, everything is 50% off. Granted they're sold out on a lot of things, but you can still find some great things, I just got The Girl Who Leapt Through Time for $10 today.

I want to see that very badly, but I am completely against buying single DVDs of a show, never understood how they could get away with doing that here and charging so much for them, I always thought it was completely retarded. So I will get it when it comes out together in a nice box set.

Hmm, old topic reborn... interesting.
... most titles should be links to their respective wikipedia article, if you want to know more.
Some favourites of mine:
Cowboy Bebop
and the movie: [url=http://en.wikipedia.org/wiki/Cowboy_Bebop:_The_Movie]Knockin' on Heaven's Door[/url]
Ghost in the Shell
movies and [url=http://en.wikipedia.org/wiki/Ghost_in_the_Shell_2:_Innocence]GitS2: Innocence, and the series [url=http://en.wikipedia.org/wiki/Ghost_in_the_Shell:_Stand_Alone_Complex]Stand Alone Complex[/url] and [url=http://en.wikipedia.org/wiki/Ghost_in_the_Shell:_S.A.C._2nd_GIG]SAC 2nd GIG[/url]. The "Laughing Man" movie is utterly unneeded if you watch the series, as it's just bits and pieces of some episodes strung together (those dealing with the case of the same name). I should probably see the movie follow-up to Stand Alone Complex: [url=http://en.wikipedia.org/wiki/Ghost_in_the_Shell:_S.A.C._Solid_State_Society]Ghost in the Shell: S.A.C. Solid State Society[/url].
Serial Experiments Lain
Samurai Champloo
Haibane Renmei
Trigun
Other stuff I've seen and enjoyed, that are not necessarily very good, or I simply don't remember much of:
Bubblegum Crisis
various incarnations: the original, BC Tokyo 2040, Bubblegum Crash, Parasite Dolls or A.D. Police Files)
Akira
The Legacy of Sol Bianca
and [url=http://en.wikipedia.org/wiki/Sol_Bianca:_The_Legacy]series
Fullmetal Alchemist
movie and series
Neon Genesis Evangelion
Noir
Hellsing
... I have surely seen more, but I can't remember any more titles