Most airlines allow only one piece of carry-on luggage plus a personal item, and the size of the carry-on is pretty much standard through out the world; there are exceptions of course. The rule comes up more often in the US only because pax try to break or bend that rule, and, of course, with heightened security, carryon luggage has become more troublesome.
Carry-on luggage is problematic on US flights because US passengers, especially frequent flyers, prefer to take everything on board and not check luggage whenever possible - maybe because pax are in a rush and dont have the time to wait at the baggage return, maybe its because in the US pax frequently have to transit a hub city between origin and destination (increasing the chance that a bag will be lost or misrouted), or maybe its just a cultural thing - who knows? In Europe, passengers seem to want to check everything in, including small tote bags and the like.
But the carry on problem is certainly not unique to the US - intra-Brazil flights are a disaster (luggage is still weighed there) so pax try to bring all the excess on board....its especially bad on flights to/from cities like Manaus and Iguascu with are (or border) tax free zones where many items, including electronics, are cheaper.........on one flight, a person was trying to bring a boxed 27"television onboard as a carry-on. Some flights between the US and Carib/Central America also have carry-on problems as people leaving the US after a shopping trip have far too much baggage.......when BWIA started flying the 738, one of the problems was the lack of carry-on space on board.