Apple's iPod is the market leader for portable music players. And the entry price just went down. If you go to the Apple Store's online refurbs section, you can pick up one now for $39 (plus tax and shipping). That comes with the full factory warranty.
True, it's only 1 gb and has no display of what song is playing. But it's the smallest player out there - with the best software interface. Get a good pair of headphones and you will be amazed at what great sound can come from such a small package!
I don't have one of these little puppies, but it is very tempting to grab one!