I've had something weird happen these last couple of days, on three separate occasions so its already too much to be a coincidence.  My mouse will suddenly freeze up; that is to say the little icon on the screen will freeze up, and won't move. The Keyboard continues to work.
It doesn't seem to start working again no matter how long I wait (though I didn't wait more than a few minutes), but if I unplug the mouse (its a non-USB mouse), and then plug it back in again, it will start working again about 50% of the time (that is, sometimes it doesn't work the first time, and I have to unplug and plug it again).

I will note that the mouse is optical, so its not any problem with the rolly-ball thingy.

When this has happened, I haven't been doing anything with the computer that I didn't before. I will note that thus far, every time its happened, I've been running skype and talking over webcam and mic with The Wench.   But I was doing that before too, and this hadn't happened until now.

So, any hints? Is it just that the mouse is crapping out? Its about 3 years old, but never had a problem before. Or is it a software thing? Or worse, something to do with the hardware of my tower?

RPGPundit

Reload the drivers, shut down everything except Skype, try a different mouse (if you have another), but likely you would be best served by dropping $30 on a nice USB mouse and not worrying about it.

EDIT:  Forgot to mention; if it is a PS/2 connector, it isn't good for the mouse or the motherboard to plug and unplug that while the system is running.