Most household circuit breakers are 15 Amps, which at 120 V translates into 1800 Watts. So you can plug in up to 1800 Watts into a single circuit (which is usually all the outlets in the room, and sometimes adjacent rooms).
Where you can get into trouble is if the electrician used substandard wiring, or if someone modified the circuit breaker with a higher amperage breaker. Both can result in more electricity being sent to the outlet than the in-wall wiring can support. The wire overheats from all the current, melts its plastic insulation, and starts a fire. The same can happen to a substandard extension cord, but most power strips use hefty wiring and have their own fuse/breaker.
Add up the wattage of everything you've plugged...