I downloaded a file with a .dmg extension. Does anyone recognize this extension?

.dmg is an extension for lot of things mac os x, so unless you got a mac, you're screwed up.

Yep. More specifically, it's a disk image (so it can hold other files and folders in the same way as .zip files etc.). Under Mac OS X they're opened and mounted automatically using the Disk Copy app. I don't know of any .dmg-opening apps for other platforms, but then the contents probably won't be any use on other platforms either.