Gamers! School, comedy - Great start to the show with a freeze frame of people making funny expressions xD Really very funny, highly recommend.
Jigoku Shoujo - Yoi no Togi - Supernatural, horror. Lit. "Hell Girl", I really like the concept of the show, reminds me a little of Death Parade. A very unique anime, highly recommend.
Made in Abyss - Adventure, fantasy. Quite an interesting concept, I'd take a guess at it being a game originally. Really quite interesting, worth giving it a shot.
Nana Maru San Batsu - School, comedy. Funny show about a Quiz Club, if you like comedies you'll probably like this one.
Princess Principal - Adventure, action. I like the concept of the show, nice action, good characters and art and a nice touch of comedy thrown in. Recommend giving it a shot.
Saiyuki Reload Blast - Action, adventure. Quite a good anime with a nice bit of comedy thrown in but it just didn't quite catch my attention. Might be interesting to fans of action/adventure anime.
Shoukoku no Altair - Adventure. Quite an interesting anime but like the above just didn't completely catch my attention. Might be worth a gander.
Tenshi no 3P! - Music, comedy. Treated to a nice bit of rock music at the start. If you like the combo of music and comedy with cute characters thrown in then this is probably the anime for you.
Vatican Kiseki Chousakan - Mystery, supernatural. I think this has only really caught my interest because I'm Catholic

It's a pretty interesting show about trying to mythbust miracles basically. You start off with the classic stigmata and crying Holy Mary statue
Youkai Apartment no Yuuga na Nichijou - Comedy, supernatural. Nice funny anime about a college student who moves into a dorm and finds out it's inhabited by ghosts and whatnot. Recommend if this sounds like your kind of anime.
Youkoso Jitsuryoku Shijou Shugi no Kyoushitsu e - School, err? Possibly a less messed up version of Danganronpa

I like the concept, it intrigues me. Recommend giving it a go.
Think that's everything!