One common use-case for multicore processing on the desktop and elsewhere is “doing many things at the same time”. You could be running many user-interface programs at once, like the “typical today’s teenager template” of tens of IM clients, web sessions, email conversations, music and video players, downloading movies, etc. Or it is a more business-like background indexing of harddrives, backups being taken, downloading large business files, compiling software, updating source code repositories, etc.
I have been doing both of these modes to some extent, and the main problem with them at least on a PC is that while the processors might be good at multitasking and sharing the CPU load, my IO system is annoyingly non-parallel.