ExtremeTech shares my opinion that most digital audio players come with crappy headphones so they reviewed in-ear sound-isolating headphones from Etymotic Research, Ultimate Ears, Shure, and Koss.
They aren't cheap, but they'll give you a way better experience. Although it should be noted that many of these solutions will cost you more than the average digital audio player!
The best sound-per-dollar value is in sound isolating in-ear earphones, which are made to slip into your ear canal and reduce interference from external sources. They can deliver some truly remarkable sound and fit into a pouch that's probably no bigger than the music player you're pairing them with.