All of them are from anime. The only non-anime songs I know is from SCANDAL, which is Shoujo S and it became an opening for BLEACH. D:
EDiT: Oh ! Everyone's posting from animes.
Kimi no shiranai monogatari - supercell / Bakemonogatari ED
staple stable - Chiwa Saitou / Bakemonogatari OP1
Listen!! - HTT / K-ON S2
No, Thank You! - HTT / K-ON S2
Super Driver - Aya Hirano / Haruhi S2
Kimi no Hitomi ni Koishiteru - Shizuka Itou / Amagami SS ED1
Complication - Rookiez is Punk'd / Durarara!! ED2
Linda Linda - Mamoru Miyano (Cover) - Durarara!! Character song.
Meh, I bet everyone already knows this songs. There's more, but, yeah. xD