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Comedy/Slice of Life is a pretty muddy request. Something like Lucky Star would fall under it, but it's not something I'd really recommend if someone asked me for "comedic anime". I'm going to assume you just want funny/lighthearted anime that makes you laugh. Rev up those romcoms.
>Aiura
Azumanga Daioh
>B Gata H Kei
>Baka to Test to Shoukanjuu
Hataraku Maou-sama!
Hentai Ouji to Warawanai Neko
Kämpfer
Kimi To Boku
Kiniro Mosaic
>Koe de Oshigoto
Love Lab
Lucky Star
Minami-Ke
>Mitsudomoe
Oniichan dakedo Ai Sae Areba Kankeinai yo ne!
Panty & Stocking with Garterbelt
>Sekai Seifuku: Bouryaku no Zvezda
Servant x Service
Turning Girls
Watashi ga Motenai no wa Dou Kangaetemo Omaera ga Warui!
Yahari Ore no Seishun Love Comedy wa Machigatteiru.
Yuru Yuri
Greentexted those I consider especially funny.