I don't think it's unreasonable to expect great sound in that price range. Not audiophile but good.
The Sennheiser HD201's are a great buy in the $20 range, are over ear, and respond quite well to EQ to take off some rough edges. They have exceptional transparency and build quality, require a little bit of juice to drive well but don't need an amp, and works well with most kinds of music.
I just bought a pair of Sennheiser HD418's as well for $30 that do good justice to metal music but they have veiled highs and a little too much bass.
For the money, save up a little more and get Sony MDR-V6 for ~$75 They are the best headphones you can find for less than $150, sound great, are bomb proof, and their sound is very flat with good detail and a comfortable bass oomph without being boomy.