You could use a relay.
I have a question. I have a swamp cooler which has a two speed fan on it which is wired to a switch that turns it either on high or off. It's load is 11.5 Amps. Is there some kinde of remote control available to switch this big of a load between high and low? I'd prefer to not run a 14/3 cable. Ideas?
As I understand the problem, you want to install a remote switch of some kind that will allow you to control the swamp cooler and allow the full OFF-LOW-HIGH-OFF sequence. If that's the case, you've got to install a switch and run a cable of some kind.
The simplest way by far is to run the 14-3, but you could install a simple pushbutton switch, and run a small wire to pick a stepping relay that would advance one position with each push of the switch.
Another possible solution is a wireless controller of some kind, a la the X-10 family, or maybe something even fancier these days. Start with Google.