said. There is anime related music out there that would stand up to "regular" music. Yoko Kanno comes to mind as does Jo Hisaishi. Harlock has an epic, if not particularly hip or usual, soundtrack. The Pillows on FLCL's soundtrack is an actual band as is Tekkon Kinkreet's Plaid. Aria's soundtrack isn't something you'd hear on the radio but it has many good instrumental piece.
That said, I am also guilty of listening to crappy j-pop music that I like solely because listening to it reminds me of whatever anime it's from.