you have really many great not adult animes out there
e.g.:
if you like ROMANCE, then i would recommend you these:
-5cm per second (an anime movie tho :PP)
-natsuyuki rendezvous (it has a sadly taste to it)
-Tonari no Kaibutsu-kun (really cute and funny !!)
-Kaichou wa Maid-sama
COMEDIE:
-the melancholy of haruhi suzumiya
-Danshi Koukousei no Nichijou
-angel beats
-uta no prince sama (reverse harem-but not really much romance :PP)
ACTION:
-ao no exorcist
-black rock shooter (idk but for me it had a little mystery involved too ;))
-one piece
-k anime
-to aru kagaku no railgun
TRAGEDIE/sad ones :PP:
-anohana <3
-clannad
-ef a tale of memories
SPORTS:
-kuroko no basket
-free!
MIND FUCK/PSIHOLOGICAL :P
-madoka magica
-k anime (again)