Some interesting animes for otakus

Trigun!!!! Best anime ever

Mushi-Shi is my favorite anime by far.

Accel World and Blue Exorcist (I might be a bit biased regarding these two because Kira Buckland voices characters for both, and I have the biggest crush on her right now...)

Also like DBZ, Cowboy Bebop, Elfen Lied, Fooly Cooly. Really would like to check out Jojo's Bizarre Adventure (the aforementioned Ms. Buckland is a big JJBA fan and hopes to work on a dub version, plus I'm a big fan of the band Yes whose song "Roundabout" is featured in the end credits).

JoJo's Bizarre Adventure, Casshern Sins, Bakuman, there's a lot of pretty good anime. If you're more of a reader, look REAL, from Takehiko Inoue, top-tier manga. Also Slam Dunk, also from Inoue.

I'd recommend: Code Geass; Cowboy Bebop; Neon Genesis Evangelion; Mobile Suit V Gundam; Gundam Wing; Zeta Gundam; Jungle wa Itsumo Hale nochi Guu; Azumanga Daioh; Puella Magi Madoka Magica; Nanoha; Nadesico; Tekkaman Blade.

Well, its a no brainer, if you are an otaku, watch the anime of a popular manga.

Other than that what i can recommend that is top notch

Hikaru no go (my fav anime eva)
Hajime no ippo.
Code Geass
Sexy Commando Gaiden and 3x3 shinobuden (both are just for the LOLS)
Original Full metal alchemist (takes a while to get interesting, but it rocks)

Bleach is meh/ok gets exiting from time to time, but never super exiting. Naruto is slightly better, gets exiting a bit more often, when it does is the bomb. But then again, it has its down times (fillers), and those are just sad/lame.

Abenobashi ---> Seriously watch it.
One outs ---> Awesome
If you like soccer you could probably watch "Giant Killing" It is probably the most realistic soccer anime ever, shame they stopped after season 1 :(

Many people would say evangelion. My personal opinion: Great concept/story, not an optimal execution. Still worth the watch probably.
Death note (Season 1 only, and im dead serious, dont watch the second, take the first ending and walk away).

Trigun ?? It is very acclaimed, but i think is over rated. I mean, its fun and lightweighted, but the thing it is that is very well balanced, with this i mean, it starts decent, the mid is decent and the ending is decent, never gets boring, but then again, it never gets exiting, it doesnt have low peaks or high peaks. Still quite a nice anime to watch, just dont get your hopes high.

Hellsing ---> Probably a must for any anime fan.
Major --->(Best baseball anime ever)
Battle programmer shirase (Short anime for geeks, decent watch).

and probably the hardest for me to recommend
Higurashi no Naku Koro ni ---> Dont take me wrong, the anime stand for itself but is kind of a heavy watch, you have to pay attention to details since the story is very confusing. I couldnt watch more than 2 episodes A day , but still worth the watch.

***Edit

Tiger and bunny
Full metal Panic
Fate Stay night.

There is a great manga called Liar Game, there is no anime of it, but there is a similar (a dumber version if you will) but still viewable
Gyakkyou Burai Kaiji: Ultimate Survivor

MY favorite animes is Samurai Champloo, Hellsing and Ghost In The Shell. And the best manga ever is Berserk.