How do I select a rear deraileur for my mountain bike? I have damaged my rear derailer and are looking for a replacement, aside from replacing it with the exact same model, what do I look for in terms of compatibility.

I note that there are long medium and short cage sizes, what is the difference?

Also, there are 7, 8 and 9 speed versions.

Some models I have seen have large plastic pulleys and look like they are definitely not for a mountain bike. What is this about?
A derailleur for your mountain bike should match the specifications on the original derailleur. That is, while it doesn't need to be the same model of derailleur, it does need to be the same brand, in almost every case.

It also needs to match the number of gears, or have more intended. Meaning a 7 speed will fit for 5 and 6 speed bikes. An 8 speed will work for 7 and 8 speed. A 9 speed will work for 8 and 9 speed, and sometimes 7 speed (but no promises.) A 10 speed mountain derailleur has more limitations. It may work with 8 or 9 speed, or it may not, depending on model and brand, and other variations. It is the newest, and least tested, with non 10 speed systems.

In addition, the cage length, either short, medium, or long, should be the same as the original. If you don't know what yours is, then long is the safest bet, but you may also need to change the length of your chain. The difference between long and short cages is the amount of chain the derailleur is able to absorb, which in turn determines the size of the gears you can run, particularly as relates to the front chainrings.

The large plastic pulley derailleurs you have seen are called Mega Range derailleurs. They are generally used for department store quality bikes, or hybrids, and are definitely not intended for a mountain bike. They give a very easy climbing gear, but are low quality, and often shift very poorly.

I hope that helps. If you need more info, feel free to ask.