Electric motors

"Where can I use" - Wherever you need mechanical rotation or if you want to just for the show.

Note make sure that the power supply matches the design requirements of the motor.

That is DC for DC , AC for AC (matching phases, frequency voltage etc.)

This is something like asking :"Where can I use water. Cold water, warm water and hot water".
There are hundreds of kinds of electric motors and it would be crazy to just start to summarize them here.

When you have to choose an electric motor, I think that the first question you should ask yourself is : "What kind of electric system is available ?" AC 1ph, AC 3ph or DC ?

Why not try to search in in Wikipedia ? I suggest to type in : "Electric motor". Once you've read all what's written there, and followed all the links, then come back if you have specific questions. I'm sure that some one on this forum will be happy to help you !

Wikipedia would be a good first source. Then read a book on motors and motor controllers. Next, search the archives here, where such questions have been discussed may times. Finally, when you have a specific question that has not shown up here before, come back and ask that specific question.