Most of the time, you only have one swap file (also known as virtual memory, or the paging file). The operating system "pages" data into the paging file.
Windows usually is configured to dynamically resize the swap file, so that it can grow larger if needed (if you just keep starting programs and loading huge data files, real RAM isn't enough so Windows will just keep dumping "old" stuff into the swap file). Linux or Unix OSes generally have an entirely separate partition used for swap data.
It's not usually a good idea to disable the paging file in Windows. It doesn't reduce performance for the most part, because it's only used when you try to do too much for your physical memory to hold everything. If you tried to do that without a paging file, the OS would just say "sorry, not enough memory, close some programs". The most common time the page file gets used would be when you start up a big game like Unreal Tournament 2003 -- the OS dumps anything not game-related or required for the OS to function, into the paging file so the game has as much memory as possible. When you exit the game and go back to some other program that was running, the OS reads the data from the paging file back into real memory.