Hellsing Ultimate is pretty good, vampires and mercenaries fighting vampire nazis in modern London. Its much better than Hellsing. Blood + was pretty good and also had vampires, and FLCL is good if you like randomness. Gun Slinger Girl was depressing and I wasn't fond of it, Blade of the Immortal lacked an ending which sucks and I'd recommend neither.

First, I'm French, but
Here is a vademecum of my while life of anime:

Little (elementary-primary school)
-Pokemon, because Pokemon. But just to Jotho, then it's just money business...
-little, I watched too Digimon, but quickly dropped off, I considerated this like a crappy ripp-off
-sailor moon, I even don't know why did I watched this! Maybe because I had a little crush on the blonde :-°... Aw, youngness, Where are you now?
-CArd captor Sakura, something is better than Sailor. I remember just some things of this, but I know that I enjoyed this anime, but why? I'll
Look this again, that wakes my curiosity (and Le joueur du grenier m'a gentiment ressorti ça dans son dernier numéro, donc...)
-yu-gi-oh And beyblade because mode effect, just don't look at this...

There was some non-Asian things great though:
-Samurai Jack, just a little pearl of epicness ( and I almost writed Perl instead of pearl)
-Code Lyoko, French thing about collegians saving the world by defending a virtual world :-° Not specially great, but persistent in memories

Collège period:
-DBZ, just why did I bought the whole 42 books?
 At college, I started not liking anymore anime that I thinked puerile...

Lycee:
-Death Note, only the first part, with L is good
-D.Gray-Man
-Deadman Wonderland
-GTO

Special Mention to City Hunter, called "Nicky Larson" who got really crappy dubs!

And sorry for necro, but I can't throw away for indefinite time my past, I must talk of it without becoming aggressive, or blurry, avoiding. It's for me, a step.
Than you to have red my post!

To finish, my recommend list:
-GTO
-Deadman Wonderland, but behave: guts and blood
-Nicky Larson in French for da lolz

I'm a bit of a Sailor Moonie myself. I've seen about 150 of the 200 episodes, but the Black Moon Circus Arc is reallly slow, which is why I haven't really watched much past it.

Code Lyoko's pretty good too, but I haven't watched most of it.

And Deadman Wonderland is fantastic! I'm in the middle of watching it myself.

Some of my personal favorite animes are:
Code Geass: It's just a fabulous show with an amazing ending.
Shakugan no Shana: Slice of life/magical girl/romance with a kickass heroine.
Star Driver: It's very camp, and probably a little NSFW, but a great show overall.
Guilty Crown: Fantastic but incredibly sad, especially the ending.
Baka and Test: School life/romantic comedy/incredible amount of comedy and a fantastic cast.
Umineko no Naku Koro ni: Murder/mystery genre. Pretty gory, like Higurashi no Naku Koro ni, but it's a really good show, and they use Schrodinger's Cat to disprove the fact that a witch's battle took place at one point.

Keroro is pretty fun to watch.