In most cases, you can technically replace an incandescent or compact fluorescent bulb with an LED light, as long as the socket is the correct size. There are some considerations and reasons why you might not want to do this. One thing you need to check is to make sure that the wattage of the LED is appropriate for the fixture.
LEDs are much more efficient than incandescent bulbs. A 15-Watt LED lamp can put out the same amount of light as an 80 Watt incandescent bulb. An 11-Watt LED can replace a 13-Watt CFL bulb or a 60 Watt incandescent one.
While you can place an LED in the same socket as an incandescent, it is not necessarily a good idea. One reason is that new sockets that are designed for LED bulbs have a piece of aluminum to act as a heat sink that can dissipate heat and keep the chip cool. A socket designed for an incandescent bulb does not have this and can overheat the LED and shorten the lifespan of the LED significantly.
Also, if you are plugging them into an old dimmer, they might not be compatible with your new LED bulbs. While you can technically fit the LED into the old socket, it is not necessarily the best idea. Doing something that shortens the life of your LED defeats the purpose, so it is best to use a socket designed for new LEDs.