Do they really work? Do the cancel out the very low tones? (Boom Boom)
How do they work? 
I own a pair of relatively high-end ones (well, expensive ones in any case. Birthday gift.), and they definitely do work, to the point I more often than not can’t hear my SO talking to me from across the room while I’m wearing them (which irritates her to no end :)).
Low tones are no problem. I find that the only thing they can’t really cancel are rapidly modulating tones (e.g. police sirens). Which makes sense : I’m not expert by any overreach of the word, but the way I understand how they word is they pick up external sound sources and broadcast their exact accoustic opposite into the audio feed so that the sounds cancel each other. I expect it’s not a surgical, point-to-point cancellation, but rather that the headphones generate a kind of white noise opposite the general/average frequency band in which a given external sound is broadcast. And so high/low/high/low would sort of confuse or defeat the algorythm as by the time the cancellation kicks in the siren has already switched to its second tone.
But trucks passing by or a jackhammer down the street ? No problem.
I’d like a recommendation for light-weight noise cancelling headphones suitable for travelling on airplanes, preferably in the $100 range.
Thanks for the replies. 
Note that there are two types - noise cancelling, and noise blocking. Noise cancelling headphones work by sampling the outside sound and generating a conflicting sound wave that cancels out that noise. They work great with a mostly constant low rumbling, such as airplane engines.
Noise blocking ones act as a physical barrier to dampen the surrounding noise.
If your headphones reduce your ability to hear other people talk, they are most likely the blocking type, not the cancelling type.
I have a pair from Ryobi that cancel out high and low range while amplifying voice range. Rechargeable batteries. Keeps the shop noise down and lets me here people talking in the next room. 4mm port for phone or MP3 player. They meet OSHA hearing protection even wile turned off.
Sorry Fear Itself but their not small or light weight but the run around $50.