In no particular order:

Evangelion

Eureka 7

Samurai Champloo

Naruto

basically just Pokemon for me

A lot of people here seem to have their anime viewing limited to Cartoon Network.

Anyway, in no particular order and off the top of my head so I'm likely missing stuff:

Azumanga Daioh
Gankutsuou
Macross
Full Metal Panic
Full Metal Alchemist (I watched this in a single night)
Kare Kano
I My Me Strawberry Eggs
Mai Otome (not a big fan of Hime though)
Maria sama ga Miteru

Lately I read more manga than watch anime though.
Angel Sanctuary
Bleach (will stop purchasing as soon as the first storyline gets finished... if it ever does)
Hot Gimmick
I's
Cain Saga/Godchild

I dunno, although a lot of people like some of the animes that have come to America (Yu Yu Hakusho, One Piece, etc.) that doesn't mean they are watching the (usually awful) dub'd versions. I've seend dozens anime series in my life, but that doesn't mean I only like the obscure ones.

Anyway, Azumanaga Daioh is hilarious. I haven't seen a few of yours, but overall some great picks. Gankutsuou is good also (very much an off-the-beaten path anime). I's is a great manga you don't see people mention very often. Bleach has an okay Manga, but honestly the anime for Bleach is better than the Manga. The storyline gets less interesting after the Soul Society Arc though unfortunately. Assuming you also liked Paranoia Agent based on your avatar.  It's cool to see so many people respond to this topic. :) 

i agree!!! watched the anime. couldnt wait and went and read all the manga so far. awesome series so far.

 i swear someone mentioned 'bible black' as part of they fav anime list.... when did we startin including h-stuff in this thread? =P

IMO bleach manga = bleach anime.... both oka... with manga no fillers. 'some' action scene in the bleach anime is done realli well.

for naruto , manga > anime.

but i think for lotsa thing manga > anime. so i'm bias in my opinion ^^ll

did anyone mention saint seyia? shaman king? (even tho that got cut/cancelled)

one of my all time fav is dragon quest dai no something manga. i think only some of it was made into anime...

Oddly enough, I tried watching Bleach and I didn't like the voices. And I'm referring to the Japanese voices. After 10 volumes of the manga, I just had ideas of what they would sound like and a number of the voices don't really fit for me.
I watched the first two episodes of Claymore and didn't care for it. I've got a ton of fansubs on my computer so if an anime doesn't grab me in the first few episodes, I usually have to give up on it.
And naz, I love Gankutsuou for the art style more than anything else. The twist on the Count of Monte Cristo was also pretty interesting. I've been trying to watch Romeo x Juliet to see what they do with that but I haven't had a lot of time to watch anime lately.

Claymore is kinda slow for a few episodes then it picks up at a ZOMG pace. Seriously, it's one of the most action-oriented anime ever. And yet, it still manages to have a great plot. Really, don't give up on it. It's great.

 LIE!!! :P It is just not possible.

Mine are:

Naruto (manga is better) 

Inuyasha

Death Note

Berserk

Hurouni Kenshin (specially the OVAs) 

Naruto, Bleach, Fullmetal Alchemist, Samurai Champloo, Inuyasha, Evangelion, Eureka 7, Fullmetal Panic, and many more cause my brain is starting to hurt now thinking about all the anime I watch, I currently putting a Naruto episode on my 2 GB Memory Stick for my PSP!!