I used to get problems with Palmolive shaving sticks, when I kept them in the metal containers in my shaving kit for too long. That was mostly drying out, cracking and smelling a bit musty.
A lot of modern soaps now carry a "months life" number or some sort of "use by", but I don't think that I've ever finished one within the time. In fact, I've just finished one which is about 7 years old, and used intermittently, and it's as good as the day I first opened it. I rarely use tubed creams, but recently finished one after about 10 years, but they aren't open to the air and must therefore store well.
On some soaps, I think those with tallow in them, a surface bloom develops when they haven't been used for a while, but this disappears in the lathering and everything is as normal.
I managed to buy a number of the L'Occitane pucks, that came with the aluminium bowl, before they ceased production, and they've been around for a good few years without problems.
In short, as a "snail's pace" user, all my soaps and croaps have held up well over time, in both scent and lather performance.