OK, SS and tube amps are completely different in how they react to impedance mismatches.
SS is pretty straight forward: with most amps, any impedance higher than the rated impedance will result in less power but no damage. Most amps have a minimum impedance, less than that will overtax the power supply and burn something out. The exception is some class D amplifiers, like the Crate Powerblock which didn't tolerate a larger load very well for some reason (it'd shut down intermittently when running into a 16 ohm cab from the 8 ohm output).
Tube amps are tougher because there's a lot going on in there. First off, they deal with VERY high voltages, like up to 650v DC. This means that you have to be careful what you do, it CAN come back to bite you. Secondly, the way a tube amp works is that the internal resistance of the tube (usually in the 4-6000k ohms range) needs to equal the external resistance (4/8/16 ohms) approximately. I say approximately because the range that a tube can operate in can safely vary quite a bit, so a tube that's biased in the middle of it's operating range can live with output impedances that are somewhat higher or lower. As the output impedance goes up the tube essentially acts as if it's biased colder and it's output drops. As the impedance goes down, it's like it's biased hotter and eventually the tube plates melt (not a good thing). The limit on how low an impedance a tube amp can stand is mostly determined by how close the tubes are to their bias limit, but for most amps it's OK at 1/2 the rated impedance (like running an 8 ohm Fender amp into 4 ohms, which most of them were built to tolerate, or even running a 2 ohm Super into 1 ohm!). The other problem with impedance mistmatches comes from the fact that a speaker is a motor. It turns electrical power into physical movement using a magnet and an coil. When the power is turned off (when the sine wave of input voltage crosses 0) the speaker cone collapses back to the neutral position. This coil moving in a magnetic field results in a "back EMF) voltage, equal and opposite to the voltage that the tube originally supplied. It's multiplied thru the transformer, so a few volts at the speaker becomes 100s or thousands at the tubes. If the impedance mismatch is bad enough, this back EMF will cause arcing thru the transformer, tube sockets or capacitors. This is even more destructive to the amp than melting tubes. Most amps will survive a 2X mismatch upwards, too (a 8 ohm output into a 16 ohm speaker) but most authorities don't recommend going any further than that.