Most of the songs that I think that are very good are already on the list, so these are my suggestions for now, which might not be in the list. (Too lazy to put youtube links in the meantime)
KARMA - bump of chicken (Tales of the Abyss OP)
Hekireki - Last Alliance (Hajime no Ippo: New Challenger OP)
Tune the Rainbow - Maaya Sakamoto (Rahxephon Movie Theme)
Mebae Drive - Marble (Hidamari Sketch ED)
Through the Night - Arimachi Masahiko (Outlaw Star OP)
Hayate no Gotoku! - KOTOKO (Hayate no Gotoku S1 OP1)
Kimi no Uta - Abingdon Boys School (Tokyo Magnitude 8 OP)
Dive in the Sky - Sakai Mikio (Planetes OP)
This is my Road - Kanon (Guin Saga ED)
Nanka Shiawase - The Oystars (Flame of Recca OP)