Depends on what you are talking about, if you have a multi strip with a built in breaker, I think they are usually around 5 amps. Most circuits in homes are 15 amps in the breaker box, some newer homes run 20 amp circuits. The outlets themselves are all at least rated for the circuit they are supporting, you will need at least 15 amps to melt an outlet but wuold probably take more due to saftey ratings.
Look in your breaker box and see what the breaker is rated at, the breaker will pop way before you melt anything with too much current, unless it is wired incorrectly.