I was sat in the shopping centre this afternoon listening to a busker and he made this way through 4 songs before stopping to eat his lunch and somehow made them all sound the same.
As there are only there are seven basic notes, A,B,C,D,E,F and G and there are only a set number of ways to go from one to another, at some point there will come a day when all the music it's possible to write has been written.
I imagine someone somewhere has worked out how many tunes are possible with the set number of notes and chord progressions, it is way beyond my limited grasp of maths, but as we have had music for so many centuries, we must be reaching a point where the same tunes are being rehashed.
Reggae bands foresaw this problem a long time ago and just made all their songs the same tune and there are many bands that use the same 'sound' which is a polite way of saying doing the same song over and over but either speeding it up or slowing it down a bit.
I don't have a problem with bands reusing the same song if it is a decent 'sound' to start with, the Ramones deviated very little from the few tunes they had, Red Hot Chilli Peppers and Green Day don't do much different either but the basic tune they use over and over is a good one so they can get away with it.
Another approach is to steal songs off other people and try to change it just enough in the hope that people don't notice or to just outright make another version of it.
What this all means is that while we are running out of many things, music is another we can add to the endangered list.