Interesting idea. I couldn't find a way of doing this, and when someone asked the same question in Adobe's forum six months ago, nobody could come up with an answer! Maybe the next release....
Anyway, closest I could get was a not-so-simple copy and paste. Use the Slice select tool to select all slices, and in the Slice palette (not the menu), there is a fly-out menu that gives an option to copy slices. Why they couldn't use the normal Edit > Copy I'll never know. Anyway, just open your other files and use Paste Slices from the same menu.
There is another facility for Saving Slices (Slices > Save Slice Selection), but this can only be used within the one document, so it's pretty useless for what you're talking about. I have to say, this is one Paint Shop Pro feature I've used in the past, and it's been a real time saver. Pity Photoshop hasn't included it.