Travel headphones need to be...

Sennheiser PX-100, I love mine.

http://www.sennheiserusa.com/private_headphones_mid-size-portables_502816

Tx Gb,
Found few in the $30-ish range on ebay new. np to try i guess!

Agree with Gb24's recommendation of the Sennheiser, you won't find anything more comfortable and the next step up in the line, the PX200, is still within your budget.

If you're going to be flying and are interested in active noise cancellation the PXC250 works very well at the price and has the same design as the 100 and 200, with the addition of a battery case inline in the cord. None of the three provide maximum isolation on their own so the noise cancellation is a nice addition.

Sennheiser HD 238, sound very good, very comfortable. Online can be found within your budget.

Koss Porta-Pro or Sporta-Pro

Inexpensive, small, foldable and very good sound for their size. Plus, if they break you can send them back to Koss with a check for $6 and they'll send you a new pair. Lifetime warantee.

Enjoy

second the porta pro--extremely comfortable, fantastic value. the sporta pro, which have a sealed plastic design, just don't sound as good. i also owned the sennheiser px-100 (until consumed by a pitbull)--they were also lightweight and good, though i preferred the porta pro, which had a bit more slam.

Porta Pro didn't work.
Finally finished my headphone amp project based on Texas Instruments 2V amplifier module.. Auditioning earspeakers with my newborn DIY amp I stopped on Ultrasone ICans. The dynamic headroom of these earspeakers allows to use wide power range and they sounded FANTASTIC amplified vs. PX200. Plus completely fatigue free and ultra light weight, completely foldable as well.

I second the Sennheiser PX-100. Great with the iPod, even better with a portable amp.

I agree with all the posts so far - they are good sounding ones, but I stopped listening to headphones, 'cause Doctors are saying they ruin your hearing...
I would recommend trying a small powered speakers to travel with, like audioengine a2 speakers.

I guess travel headphones should be noise cancelling, so AirPods won't suit noisy trips I guess. I don't know what design you prefer, but different travel blogs confirm that  MonoDeal headphones are perfect for travelling (the price is rather loyal, about 40-50$ ).