I'm talking like bands that were pretty big and had radio success that had some great songs (non-singles) outside of what was heard on the radio.

Like for instance, I really like the first Third Eye Blind blind album but not really for the singles.

God Of Wine
http://www.youtube.com/watch?v=KLEXgfoVqB4
the last half this is too good

and their second album had Wounded on it which I think is a pretty incredible song (love the use of harmonics).
http://www.youtube.com/watch?v=XTKM4EEfb68