In comments, David Glassborow makes the excellent point that the hard drive, far more than the CPU, seems to be the limiting factor for the concurrent revolution. When your computer is frustratingly slow, the odds of your disk-access light being on are approximately perfect.
I know very, very little about hard drive technology, but I am under the impression that all hard drives are strictly serial in their processing -- that the hard drive processes only one request at a time and that requests are serviced in a FIFO manner.
I absolutely expect to see parallel hard drives emerge. Naively, it would seem fairly straightforward to have multiple heads per platter and and expanded bus so that multiple simultaneous read/writes could be serviced. In a sense, RAID 0 in a single bay.