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).
I originally thought I had a hard drive that was going bad, but then I bought a new hard drive and the problem didn't go away. I had some malware several months ago and I'm fairly certain that it corrupted some of my Windows drivers. I tried doing a repair reinstall a while ago but it didn't fix the problem, so I think I'm going to have to do a clean reformat / reinstall to fix it.
Although your comment about 0.93 being just around the corner makes me wonder if I'd be better off waiting a little longer for that stable version of it to come out.