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
Love Live! school Idol project
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
Kuroko no basuke
Kimi ni todoke
Say I love you
Uta no prince-sama
Kaichou wa maid-sama
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.