I was wondering how many counting songs people could remember from their childhoods (or later).

Besides the well-known 100 Bottles of Beer, (more on that in a moment), I've known a Passover Song (Chad Gadya), a Gospel Song (the title escapes me) and others. Songs have been a way to teach counting for a lot longer than books have.

Any examples out there?

Now, about that 100 bottles...

I have a version that applies to my profession, and goes like this:

100 bugs in the program code
100 bugs in the code
Fix one bug and re-compile
101 bugs in the code

...and so on.