Travel headphones need to be...

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$ ).