I bought the Sennheiser HD 280 Pro headphones a few years ago, and they are great. Someone who had been researching headphones suggested them to me (instead of high-priced Bose), and I have been very happy with them.
I don't think they are technically called "noise-cancelling" at the Sennheiser site, but good enough for me, no problems whatsoever, and Sennheiser makes some very high end phones, so they are surely less so than the top end ones. Note the design, the hinges, how if you placed the headphones face to face, then push them up into the over-the-head part, they fold up nicely, very compact for traveling.
Here is a Google search. They are always available at less than the suggested price $149 ($76.25 it seems now at Amazon):
hd 280 pro - Google Search
Last June I also bought the Shure SE215 in ear headphones and also like those a lot. Here is a web page I had saved when I bought them for $99 (which appeared then to be a good bargain for as high a quality as they are):
Shure SE215 Earphones Black
I bought these for even greater convenience carrying around (even less space required), versus the Sennheiser over the ear. They do a great job of blocking out noise. As a matter of convenience though I still prefer the over the ear, versus plugging them into my ears, but again bought these since they took even less space carrying.
At home or away I generally like to just use the Sennheiser to block things out, if I had my druthers. The Sennheiser ones also have a long, telephone like cord, that I find convenient, generally out of the way but the ability to stretch. On the Shures the cord goes up over the ear, between your head and your ear (note, for example the one labeled Right here, how the cord goes back), which holds them in place very well and helps maintain the seal. (One review I read was someone in NYC who wears them in his sleep.) It makes them more of a hassle putting them on though, than the over the ear Sennheisers, and I have generally always found over the ear design more isolating, say better able to focus on work or study, for whatever reason.