Editor's Note: This tip was updated on March 4, 2010, to indicate that the correct command name should be MatchProp (Match Properties). The description below reflects this correction.
Frequent tipster Leonid Nemirovsky notes that if you have several drawing files open, it is possible to use the Match Properties command (from a pull-down menu, buttons, or the command prompt) between them.
"Select the source object in one file, hold down Ctrl, and press Tab to switch to another drawing. MatchProp is still in effect; select a target object, and it will work. However, this trick will not work between paper space (PS) and model space (MS). For example, if the source object was in MS, then the target object must be in MS also. As soon as you try to switch drawing spaces in the target file, you lose MatchProp."
Notes from Cadalyst Tip Patrol: It works! I had different results from those described above when I went from paper space in one file to model space in another. The process would work just fine, as long as I didn't switch drawing tabs. Even when I was in the same drawing, I would lose the Match Properties command when I switched drawing tabs. But, just as Len said, I could use Ctrl +Tab to switch between open drawings. Make sure you are in the correct drawing tab first, then switch to the source file, start the Match Properties command, and use Ctrl +Tab to move to the other file.