I've been playing the piano for a long time, but I don't ever recall seeing any piece of music call explicitly for the soft pedal. Some digital pianos and keyboards don't even have one. I know there are terms for it in classical notation though, such as 'una corda' or 'due corde'.
How often does it actually appear in scores? Was there a period when it was more commonplace?
I would say the more recent the music, the more often it's notated (at least in classical music). In modern music it is very common but it was used already at least by Beethoven. For example, in the 4th concerto, you can find all of una, due, and tre corde in the second movement. Liszt certainly used it; check the beginning of the Liebesträume, for example. Debussy and Ravel often write "2 Ped" to mean you should use both the damper and the soft pedal. An example can be found at the beginning of Ondine in Gaspard de la nuit. Or they may write sourdine as in the next pieces of Gaspard.
