I think the most common practical problem for sorting large amounts of data is to enable efficient search operations later, for example binary search over sorted data.

I also agree that needing to sort large amounts of data fast is actually not that common a requirement.

EDIT: I would add that the speed of sorting on CPU is often underestimated. See my blog post about fast multithreaded radix sort on CPU here: http://www.forwardscattering.org/post/34