Just to get technical...

Yes, stereo amps need a load on both channels, though if you can prevent the side with no speaker from being 'driven' - turn the volume off! - it will be okay as the load is only required when a signal is present.

Putting a shorted jack into the effects loop (on a mixer-amplifier) may also cut off drive to that channel, but be sure you know what you are doing!! Don't short the amplifier output!! If it's a slave amp, just don't plug the input lead in on the unused side...

Mono amps are okay with just one speaker, but you must be sure the single speaker can handle the extra load...

Two eight ohm speakers on a 100w amp must be able to handle 100w between them, but one eight ohm speaker on the same amp is likely to be subjected to around 70w because the load is inductive, not resistive. In other words, Ohms Law doesn't strictly apply - there are other considerations.

Ooops! Another can of worms!! ;o)