I've considered flying Thor to NYC a few times, but I've always chickened out b/c it's a five hour flight. I'd rather try him on a short flight first, jic. Maybe next time, though.
I see people walking dogs around airports, and I always ask them about how it works, and they always say it's fine.
As others have said, the dog has to be placed under the seat in front of you... so you have to make sure you have a seat that allows that. I'm lucky enough to fly first class often, and have not been able to bring Thor because all baggage has to go overhead.