There's an odd idea on this thread that one has several bikes, including a rigid singlespeed and a geared full-sus, and you select the "right" bike for the trail in question from among the selection available based on their performance.
That is insane. Almost invariably, the geared FS is going to be quicker (in the hands of the same rider) over almost any rough trail than the SS and the rider of the SS is going to get beaten up more and have more sketchy moments, more stalls, more refusals and quite possibly more scuffing, bruising and bleeding going on.
There is probably never a right situation or a perfect trail for which to pull out a rigid singlespeed on performance grounds. (although in reallty clarty mud when you don't have time to do any maintenance you can make something resembling a case for it).
If you like riding a singlespeed bike without any suspension then it is appropriate whenever you fancy, and if it's the only bike you've got then you don't get the choice anyway.
What is it that meerkat says? 🙂