Repeated overloading of your wiring system will degrade a number of components from the connectors, to the jacketing, to the insulation, down to the wires themselves.
It ain't a smart thing to do, of course, but it's unlikely to do any real damage as long as the breaker is correctly rated, the cables are the correct size, and you haven't actually created a dead short. A 2x overload (say, 30A drawn through a cable rated for 15A) for a few seconds
will generally cause an insignificant temperature rise. Problem is there are a lot of "ifs" in that sentence and no actual installation standards in Taiwan - at least, none that are taught or enforced. It's up to each "electrician" to make it up as he goes along. Also, the crappy US-style plugs and sockets they use here (laughably rated at 20A) are inherently unsafe.
Best thing to do is just use your common sense - don't leave any high-power equipment unattended (or, come to think of it, any other sort of equipment), and don't overload sockets or add excessive socket strips.