Pluggd into15 amps you can run a vacuum (You normally do soon a 15 amp circuit in the house) Televisions and the fridge(Though fridge and Vacuum at same time, depen ding on vacuum, may get you clicked off, no damage, just darkness)
The only thing likely to be damaged is your pride as you hike yet again into the house to re-set the breaker...
Air conditioners.. You MIGHT be able to run oneon 15 amps. but this is the device most likely to be damaged by trying if there is voltage drop.. It also will usually pop the breaker first however.