NIKON DSLR remote control can work for any of the cameras, correct?

If i buy a remote control will it work for my D3000
and if i sell my D300 and buy another DSLR like the D5100
will it still be able to work for the D5100?

and if so what type of remote do i get?

Added (1). Sorry i mean D3000

No. Not necessarily.
The D3000 and D5100 you have a good chance of the remote working for both. Certain remotes work with certain cameras and not with others.

Wrong even within Nikon camera models, the remotes aren't always compatible to each other.

You do realize you mentioned three models in your question don't you?

Yes - If you mean the ML-L3 IR remote - it works with the D5100 and all Nikon cameras that have an IR port. This includes all of the consumer-grade DSLRs, as well as some compacts, such as the P7000.

It will not work with the pro level D3, D700m, or D300s. It will work with virtually everything else, including the D7000, D90, D5100, D3100, etc

But it's only $13 US, so if you go to a pro level camera that will not support it, it's not a big loss. It's only one of a few things that Nikon makes that is inexpensive.

http://www.althephoto.com