What are some good comedy animes?

The Devil is a Part-Timer.

Try 銀魂 and Daily lives of Highschool boys X3

Ouran High School Host Club is my number one comedy アニメ :D

Some other good ones:
Hetalia
Blood Lad (has it's moments)
Watamote
NARUTO -ナルト- (pre-shippuden)
Free!
Chobits

I find ヘタリア and Ouran High School Host Club to be HILARIOUS <3

宇宙 dandy he is a dandy guy from space!

Maria Holic! Always my first choice when someone asks for a comedy anime. Also try:
Is This A Zombie?
Air Gear (WARNING! It's really freaking stupid. Funny, but stupid.)
Welcome to the NHK! (Though that's もっと見る dark comedy.)

kashoue wa maid sama how ever あなた spell it lol

D-Frag!

Sabagebu! (pictured)
Nichijou
Daily Lives of Highschool Boys
The World God Only Knows
Princess Jellyfish
愛 Lab
Nisekoi
Senyuu.
Sayonara Zetsubou Sensei (Dark Humour)
My Mental Choices are Completely Interfering With my School Romantic Comedy
Ben-to

Well, since Hataraku Maou-sama has already been posted...

Yu Yu Hakusho has some HILARIOUS moments and 名言・格言 in the English dubbed version.

Gekkan Shoujo Nozaki-Kun (I usually don't like this sort of anime, but this one I find super entertaining-)

All the others I would have 発言しました have already been posted. :3

Toriko
My Bride is a Mermaid
Squid Girl
Saiyuki
Sakura Wars
Sgt. Frog
Fruits Basket

1)Noucome
2)Soredemo Sekai wa Utsukushii
3)Zero no Tsukaima
4)Seto no Hanayome
5)Tokyo Ravens
6)Bokura wa Minna Kawaisou
7)Mangaka-san to Assistant-san
8)My Romantic Teen Comedy SNAFU-Oregairu
9)Blood Lad