I have used a pair of Sony NC phones for four years. They cost about GBP95 and are brilliant. I have used them often on trains as well. I also use them as regular phones on a MD walkman without the NC function active.
The NC function uses a single AAA battery and last for a very long time, I only have to replace the battery once or twice a year. They fold up into their travel bag.
Any airline allows you to plug in your own phones. The Sony unit came with an adaptor for the two prong fittings used by some carriers, although I have only had to use this on LH.