I have a pair of Monoprice 8323 headphones
that have been great and they're only $23.20. I wouldn't mind something more serious, but these are compared surprisingly favorably against other headphones in the $50-80 neighborhood and I don't feel nervous about letting kids use these. My only real complaint is that the padding on the headband isn't the most comfortable, but they haven't bothered me too much.
If you're interested and want more info, let me know. These are used for primarily for general computer use, so I'd want to put in a bit of music seat time to refresh my ears before commenting too much on audio quality. They're more than decent for casual listening though.
I don't consider myself an audiophile, but I can appreciate the differences. For reference, I listen to music the most on a pair of Paradigm Monitor 7 towers, powered by a Yamaha RX-V1300, with a Slimdevices Squeezebox as the source. The Squeezebox is currently connected via Toslink/optical, since I found that I prefer the sound from the Yamaha's DACs over the sound of the DAC in the Squeezebox. FWIW, I chose the Monitor 7s over Studio 20 bookshelves for the fuller sound and because the 7s pull double duty as mains for 5.1 sources (i.e. movie duty.)