The constant hum of jet engines bothers me. Sure I can live with it for a four hour flight. But I am anticipating a flight across the pond to Europe. I sampled the Bose at an airport. Wow! But they are out of my budget. Do you have any experience with headphones that cost less?
Sony makes some decent cheap ones for less than $100.
JVC makes a nice pair that can be had for around 100 USD. My office is noisy and I’m very much in love with mine. 
I want to say the model number is HANC250.
I see many on Craigslist locally.
I bet you will too!
Forget the noise cancelling headphones and get in-ear earphones instead.
The noise cancelling headphones require batteries for noise cancellation to work (and some models won’t even play music without batteries even with the NC off). They are only moderately effective. They are bulky for travel. Their sound production is usually somewhere between ordinary and (with NC on) absolutely shit. They are monstrously expensive for any of the good ones.
Earphones are like a combination of earplug and earbud. They keep out noise passively (ie by simply blocking your ears well, like earplugs). It’s hard to get good objective figures but broadly they keep out about as much noise as active noise cancelling headphones. They keep out sudden noises (like babies crying) well and not just constant noises like plane engines, which is all active NC is good at. Their sound quality varies with price but is generally excellent. They are tiny and this matters a lot to me when travelling. I can carry them in a pocket. You can keep them in your ear blocking noise when sleeping on a plane even with our head to one side (try doing that with big ass headphones on!).
I’m a major convert. They have made a major difference to how comfortable I find flying.
Their one disadvantage is some people find them uncomfortable. I don’t find them particularly comfortable but you get used to them. The good brands come with about 3 or 4 different earbud tips of varying shapes and materials for you to try. Big NC can headphones get hot to wear anyway.
You can get a cheap pair for less than $100, and a good pair for about $150. I have Etymotics.
I agree with the criticisms of Princhester - I don’t have much experience with earphones (on plane), but had both the Bose and the Sony (not sure which model Sony as I lost them I think).
Bose was definitely better than the Sony, but eventually broke (physically - they still worked electronically - but hard to keep on head). Not sure if I can blame it on Bose or not. I think I liked the NC aspect a little more than Princhester did. You can turn it on and off - and there is a difference - absolutely, but I’m not sure it is worth the cost and the space. I would actually use them - with earplugs underneath - to try and sleep (no music). I’d be tempted to use something external in addition to the earphones - but not sure I’d spend $300 - or whatever they were again.
Maybe look for them on sale? I had a set of Logitech noise cancelling headphones that I got for ~60$ IIRC. They worked fantastically against the dull roar of our server rack, but eventually the swivelling hinges that let them lay flat in the carrying case broke and I had to warrantee them.
Though if you’re going to be listening to something else anyway, I’d say that the in-ear solution is probably more cost-effective.
Another vote for in-ear earphones. Get proper ones though - many in ear ones don’'t really isolate the noise very well - try Etymotic. Crying babies are no longer a concern to me.
I bought a pair of refurbed Sennheiser earphones the are pretty good. The NC isn’t as good as the BOSE but definitely allows me to listen to my ipod at a much lower volume when on an airplane than wo/ NC. They are much smaller than the BOSE and fold up into a pretty small case. They will work as normal earphones if the battery runs out.
If you go with full-sized headphones, I’d really recommend the over-ear type instead of the on-ear type for comfort on long flights. I had a pair of Bose for many years until they broke recently, and I’ve read the complaints about the newer models breaking, and it’s always in a spot where there is no hope of repairing them. A real drawback for something that expensive. But they worked extraordinarily well.
The Bose are expensive for a reason. I fly internationally quite a bit and you can have my Bose when you pry them out of my cold dead fingers.
I’m a private pilot and if you think inside of a jet is loud then you should try a Cessna 172 (I’m sure a P51 is even worse). I’m satisfied with my Telex Echelons but they are probably not suitable for commercial passenger use. The battery compartment is in a separate box connected by a cord, and they have a microphone. (wow - the ANR model is a LOT more than what I paid)
Don’t see any mic less models in my quick search
Brian
Moving from MPSIMS to IMHO.