You should be able to use a 16 ohm speaker with output designed for 8 ohms. Everything else being equal an 8 ohm speaker will just not be quite as loud as an 8 ohm. But it will work just fine. The output rating generally shows you the lowest ohm load you can put on the amp. So this should not be a danger to the amp or the speaker.
If you own this speaker, I don't think you lose much by trying it.
If you want it to be louder you either add another 16 ohm speaker or swap for an 8 ohm with otherwise similar specs. If you amp has two speaker outputs and you hook up one to each of the amp's outputs the amp will see 8 ohms. Still fine.
What you don't want to do is go BELOW what your output was designed for.
I don't think the ohms are the issue with mismatching speakers and cabs, but Marcel is certainly right that it can produce some nasty results.
Of course this is very general... Is this for a guitar? Are you building or replacing? What lead to this predicament?