OS X Yosemite Hangs--A Lot

I've been having an ongoing problem with my system hanging every four or five days. The only workaround I've found is to restart every three or four days before the hang can occur.

I'll come back to the iMac after having been away for a few minutes (not long enough for the screen saver to kick in) and although the system looks functional (all the open windows are showing normal activity) and I can move the mouse pointer around to my heart's content, neither the Bluetooth mouse buttons nor the Apple Keyboard (with numeric keypad connected by USB) function. My only recourse is to press the on/off switch to shutdown.

I've gotten into the habit of manually restarting every few days, but sometimes (like just now) the hang beats me to it. I think it's a Yosemite problem because it occurred with my previous iMac as well. In fact, that's one of the reasons I upgraded my iMac.

iMac Retina 5K, 27-inch, Late 2014, 4 GHz Intel Core i7, 16 GB 1600 MHz DDR3, Yosemite 10.10.3

Is anyone else experiencing this problem?