When I open files that I have downloaded from LimeWire, it opens the files in a different program than I want it to. Is there any way I can change the program that automatically opens my files?

Let's say, for example, that you want an MP3 in iTunes rather than Quicktime. Open iTunes>File>Add to Library and that will tag the MP3 so that it will play in iTunes no matter where it is currently stored. For future reference, if you want an MP3 to play in iTunes, use iTunes>Preferences to set iTunes as the default format for downloads from the internet. If this is not your problem, identify the particular difficulty and someone will advise.