There is lots of good info in this thread. If you really want anything that is close to a hard and fast rule, here is what I have ended on. (There are always exceptions and it's up to you to decide what works/sounds best for your equipment. Keep in mind that I'm also some random internet chump, so take this with a grain of salt.)
Most important is to know if the amp is tube or transistor.
Transistor amps can go higher (ie if the head is 8ohm, it can deal with 16ohm), but not lower (8ohm into a 4ohm cab will make the transistors try to pull twice as much current and they will get nice and smokey.)
I found a good piece of advice from Scott in the archives about tube amps:
The way I understand it, you can tell if you're causing a problem by running too low impedance speakers... all you need to do is play the amp like you normally would, and after a couple minutes, touch the output transformer with your hand and feel how how it is... if it's warm or even a little hot, that's alright. If it's so hot that it burns your hand to touch it, you shouldn't run that low of an impedance. I usually check the output and power transformers, both of them, after about a minute, and again after another minute or two, and again after 10 minutes or so... I've never had either transformer be too hot to touch.