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First, Death Note. Hands down, it's one of the best stories. A great view of reality and humanity.
Clannad. Really touching.
Ao no exorcist[ or Blue Exorcist ] - this one's pretty good, actually.
Naruto and Bleach - dah, obvious.
Vampire Knight
Hell Girl

My list spans more, but these are my favorites

Clannad
The Melancholy of Haruhi Suzumiya
Azumanga Daioh
Another
Dragon Ball Z
Kokoro Connect

Words can't explain why I love all of these.

Vampire Knight. It was so beautiful and everything was just gorgeous.
Elfen Lied. It was such a sad but amazing story.
Rozen Maiden. I cried like a baby ;_; but other than that, although some episodes were a bit irrelevant, the characters and plot were just perf.

Just recently watched Minami-ke. Yes, I know, it's an old anime, but I'm rather slow in following the anime nowadays... Anyway, I just can't stop watching this one.

Hmmm....Lets see...

Fairy Tail - Cause its funny and I like the characters

Durarara!! (Or is it DRRR!! I have no idea) - I just REALLY liked the characters they were all awesome

Hetalia - Cause its REALLY funny

Inuyasha - LOL YES I LIKE INUYASHA OK?!!

Jinrui wa suitai shimashita - The WTF levels of that anime are very high (when I say WTF levels I mean comedy wise or weirdness)

Natsume Yuujinchou - Nyanko-sensei....

The law of Ueki - I guess cause it was pretty funny and the powers were kind of cool

Pretty much...I don't think I'm missing anything on this list (Oh god the reasons are pretty much all the same do I really only care about comedy????)

While it may not be my No. 1 anime, the E-Card arc from Kaiji S1 is some of the most compelling TV I've ever seen. A real psychological chess match that runs 5-6 episodes without letting up for a moment.

I would have to say, Fruits Basket ( my first anime), Nana, Rose of Versailles, Gankutsuo, Cowboy Bebop, and Ouran High School Host Club, Madoka Magica....and I enjoyed both series of Fullmetal Alchemist...and Baccano.

Tengen Toppa Gurren Lagann ~ The Guys behind Neon Genesis Evangelion and FLCL make a Saturday morning cartoon involving Huge mechs powered by awesome and lots of screwing... No really it's his main weapon.

It's one of the only anime's where it's unmanly to not cry.

*edit* DO NOT google this show. Do to the awesome that is this show. Everything has huge spoilers. Hell the Screwing joke may have said too much.

definitely tonari no kaibutsu-kun and kuroko no basuke UvU

Fate Zero (the prequel to Fate Stay Night) is awesome!!!
I also like Nichijou since it's hilarious and I can totally relate with the characters.
Mirai Nikki(yandere alert) is also one of my favorites. Cool action scenes, cute(?) characters and lots of violence...lol.
There's also Baccano! and Durarara(rarara-).

These are some of my favorite anime:

Deadman Wonderland
Sword Art Online
Durarara!
Gurren Lagann
Blue Exorcist
Madoka Magica
Dragon Crisis
Acchi Kocchi

Bleach is the best anime watched so far by me. I always prefer to watch this anime online in my free time.

Always loved Nuku Nuku (the OVA, not the TV or Dash version which are only so-so). The characters are all great, insane stories, etc.

Samurai Champloo and Cowboy Bebop have held up surprisingly well in recent rewatching.
Paranoia Agent has as well - I feel like Satoshi Kon did a good job telling such a story in TV format.
Madoka Magica was a good subversion of magical girl shows.
Fullmetal Alchemist (2003) was just all around entertaining and a well-done shonen action series.
Urusei Yatsura: Beautiful Dreamer is an awesome movie (and watchable even if you haven't seen the show - I saw it way before I knew what UY was and loved it)!

Death Note, Monster, and Ranma 1/2 get honorable mentions - DN was good, but the latter half was weak; Monster is perhaps too long/slow to recommend to most people, and the humor in Ranma 1/2 may be too absurd for many.

I have lots of favorite animes! I therefore consider them to be all best. XD

-Naruto
-Gakuen Alice
-Detective Conan
-Inuyasha
-Ouran High School
-Fairy Tail

Those are just some. Oh, and is Doraemon considered an anime? Because if it it, then it tops my list!<3 It may not be as epic or as complicated as the other series, but Doraemon's episodes always have life lessons in them and they are always amusing too. I enjoy watching it for its simplicity. ^_^ When I watch it I don't have to worry about... for example, if Sasuke is ever coming back, or if Ran (my namesake teehee) will ever find out about Conan's true identity. All I have to worry about is if Nobita's mom catches him sneaking out of the house or if he does well on his exams, which are things that I can actually relate to. The show makes me feel happy and lighthearted, which is the main reason why I love it so much. ^_^