I'll mention another scenario where volatiles are important.
Suppose you memory-map a file for faster I/O and that file can change behind the scenes (e.g. the file is not on your local hard drive, but is instead served over the network by another computer).
If you access the memory-mapped file's data through pointers to non-volatile objects (at the source code level), then the code generated by the compiler can fetch the same data multiple times without you being aware of it.
If that data happens to change, your program may become using two or more different versions of the data and get into an inconsistent state. This can lead not only to logically incorrect behavior of the program but also to exploitable security holes in it if it processes untrusted files or files from untrusted locations.
If you care about security, and you should, this is an important scenario to consider.