Ok I'll just put a bunch that I like. My favorites could change as I discover more anime.

 Bleach- It's cool.  Not very original, but it's just cool. Good action and some slapstick humor if your in the mood.

Naruto- Damn filler seasons almost ruined everything.  Some good humor, but what gets me are the great fight scenes.

Yu Yu Hakusho- Hiei

Cowboy Bebop- currently the among the top non-anime favorites for a reason. Ending will make you say NOOOO.

Fooly Cooly- Well, it was weird and there were only 6 high quality animation episodes. Overall, just really funny and full of jokes you won't get the first time you see it.  Also(in my opinion) some of the best dub work like Cowboy Bebop. Very good in keeping the feel of the original version.

Death Note- Well here's one I can't shut my big mouth about.  Not action packed like the other anime's I just posted. This show falls into the genres of drama, psychological thriller, supernatural, horror and detective stuff. You might get a headache the first time they throw you one of the main characters plans as there so complicated and smart. Did I mention the main character is crazy evil.  There are some scenes that will get your attention and make your heart beat. What other show can make a guy eating chips intense. This is by far my favorite for now and probably for a long time.  When the series ended, I was begging for more. 

Some others that I like somewhat.

DBZ-long time fan favorite to many. You'll see some similarities in shows like Bleach/Naruto/One Piece as they all take a little of something from this action packed I'm stronger than you show.

Prince of Tennis-Really silly

Blue Gender-creepy if happened

Samurai Champloo- Cowboy Bebop offspring.

Edit: Oh yeah, Ghost in the Shell is great also. Too many to keep track of.

I'm gonna have to add Yu Yu Hakusho that's one of those that i forgot thanks naznatips and Donwii for reminding me....

@Bodhesatva

Don't even start with that. There are so many different types of anime's that there is one for everyone, I guarantee it. Besides, were all in a gaming forum, so you might as well post that on the front page XD

Cowboy Bebop
Ninja Scroll
Trigun
Blood: The Last Vampire
Vampire Hunter D: Bloodlust
Fist of the North Star
Akira
Grappler Baki
Princess Mononoke
Dragonball Z

 True. Except me, of course.

Some other choices I really liked on here:

Ghost in the Shell

Prince of Tennis

Naruto (minus the fillers)

Bleach (as was stated, not original, just awesome)

FLCL (fooly cooly is how it's pronounced)

I'll go ahead and add Outlaw Star and Trigun, both along the same lines as Cowboy Bebop.

Samurai Champloo (had a bad ending IMO, but a good anime overall)

A good swordplay one is Ruroni Kenshin.

I'm not big on Inuyasha, too much love story. If I want that I'll watch Eureka 7.

Death Note is an interesting one as well.

I also enjoyed sCRYed and a couple of the Gundam ones.

For those of you who do like anime and are looking for a great game with many of your favorites, I highly recommend you import Jump Ultimate Stars. http://youtube.com/watch?v=tlaJw_TUoTc That's an overview and review of the game. The only thing is don't listen to the guy when he says you need to know some Japanese. There is a full translation guide on gamefaqs. This is the best fighter ever made on a handheld IMO.

Dolla Dolla is into the more violent anime's I see.

FLCL, that's right. Fooly Cooly haha. Like I said there are too many.

It's true, I'm not gonna lie lol I like lot of action in my anime's. A good story doesn't hurt either.

Becuase you are hella cool playa

SDon't like Anima all that much. It's good, but I don't watch mauch anyways. S-CRY-ed was the only one I realy liked. Maybe Trigun.