This has happened thrice in the past hour. I have to keep rebooting, and if this continues, the game will be impossible to play.

Basically, things just freeze, but not totally. The characters still move (in that sort of lurching way they do when they're stationary) and the pointer turns into the ticking clock. Apart from that, nothing. Can't scroll or click on anything.

Has this happened to anyone else?

It happened to me once, but only during one particular battle and mostly after using the arrow keys to scroll over the map. After about 20 minutes or so things were back to normal. I went through this particular battle by quicksaving after every turn and avoiding the arrow keys. When you get the seemingly endless stopwatch, press Alt+Tab to get back to your desktop (might take a few seconds) so at least you don't have to reboot. Then you can use the Windows Task Manager to end the Jagged Alliance 2 task, start JA2 again and load your quicksave.

If this doesn't help, you could try the 1.13 mod from http://www.ja-galaxy-forum.com/board/ubbthreads.php?ubb=showflat&Number=236228 (all you have to do is to click on "Latest FULL Single Click Installer", download & install). While I haven't had any crashes or freezes with 1.13, the downside is that you will not be able to resume your save games.

I've had very similar trouble. Charachter will not walk/run, but can crouch, go prone, stand and do a few other actions. I discovered that saving, closing, and re-opening the game will solve this problem.
Considering the fairly numerous and annoying bugs in this game, it's surprising
that Gog.com sells it here.