I have some sockets that take nothing higher than a 60-watt bulb. If I use an LED or CFL, can I use a brighter bulb? For instance, a 13-watt CFL is equivalent to a 60-watt incandescent. Is it OK to use a 23-watt CFL instead? That would give me the equivalent of a 100-watt incandescent.
Fixtures have a safety rating and one should not put in bulbs that exceed the labeled rating (such as "do not exceed 60 watts"). As long as you don't put a bulb that uses more than 60 watts in that socket you will be fine.
The good news is the energy-saving bulbs that replace a 60-watt incandescent will only use 10 to 15 watts, depending on the actual bulb you buy, and give off the same amount of light. If you want even more light, you can bump up to a 23-watt CFL that will give off as much light as the old 100-watt bulb did, while still staying below the 60-watt power cutoff. You should not, however, install a 100-watt bulb, as that could cause a fire hazard.