Easiest thing would probably be to backup the full Armory data directory, if you are able to. That would save you from having to let Armory build the database again, and you will backup any wallets, transaction comments, etc.
Hrm, good point. Not having to let Armory build the database again would be a pretty big benefit to that approach, so I think I'll do that.
If you think there's any chance of a hardware issue, I'd avoid copying anything besides the wallet files if I were you.... I had an issue that turned out to be bad RAM causing Armory database corruption issues each time I tried a rebuild... copying a potentially bad database might propagate whatever problem you're having.
Also, with the 0.93 just around the corner, you can either wait for 0.93 or grab the most recent beta from the 0.93 thread which offers much faster database rebuild times thanks to goatpig's efforts (I recently did a database rebuild and it took about 1.5 hours on a HD, not even an SSD).
Even Bitcoin Core blockchain downloads with 0.10 are much better, if you choose not to copy over its data directories. It can still take a number of hours, but that's a whole lot better than the day or two it used to take.
