I rarely use my CD/DVD drive so I didn’t spot this problem for several months. My CD/DVD drive which had previously been working fine in Vista suddenly no longer showed up in “My Computer”. I tried new CD/DVD drive, but it also didn’t work. Eventually I found this KB article which solved my problem: http://support.microsoft.com/kb/314060
If you’ve had a similar experience please do read the KB article and try it first. It may save you a lot of frustration.
Although I am not certain what started the problem, deleting the “UpperFilters” registry key (see the KB article for more details) fixed everything.