Ergo proxy is my favorite. if you like dark atmosphere and cold carecters, you should watch it. i think there are over 50 episodes and you dont get bored cuz the story is fascinating. In addition, the lead anime character is a fabulous girl :)

have a nice watch..

i think everyones already listed the best ones out there, but seriously Sword Art Online is beautiful!!!! i highly recommend it!

others i watch are:

The Pet Girl of Sakurasou

Shin Sekai yori

Girls Und Panzer

Oreshura

The Unlimited

Amnesia

Love Live! school Idol project

Kotoura-san

Vivred Operation

AKB0048: next stage

say i love you

my little monster

sei ichi hastukoi

Deamon King Daiamo 

some are really old but some are recent x

Magi 

Kuroko no basuke

K-on

Vampire knight 

Kimi ni todoke 

Say I love you 

Uta no prince-sama

Kaichou wa maid-sama

Guilty Crown

I think Code Geass is really good, and I highly recommend it.

Also, you can try Fairy Tail, if you're into action/comedy.

For some romantic stuff, try Kamisama Hajimemashita, it's a very subtle and simple story. Fruits Basket and Kaichou wa Maid-sama are also worth trying out.

I've tried to watch Bleach before but it's not that great compared to the manga.

Of course there's also the very classic and well-received Rurouni Kenshin. :)

Wow, you mentioned everything that I watched that has romance as its theme :) Sailormoon is also my all time favorite. I also recommend Ranma 1/2 ,Inuyasha ,Fushigi Yuugi  and Fairy Tail if you're into comedy/romance/action themes.