A set of headphones I have been very pleased with is the Sony h.ear. They clip behind the ears and that makes them firmly stay in your ears. They are also very comfortable (I've been able to wear them for hours with little discomfort).

As far as sound quality goes, I've been pleased with the sound that I get from my pair. I'm not a great fan of bass (I almost always listen to music with no sound adjustment) but my headphones have fairly strong bass. If I remember correctly, the specs say that the frequency response bottoms out at 18hz.

I hope that helps.