Something I installed in the past month made Vista no longer recongize my DVD-RW. I tried removing it and reinstalling it but that didn't work. After a few online searches I found "Top Tip: DVD-RW driver problem in Windows Vista?".
I don't know why it works or what application made my DVD-RW stop working, but Andy2639's solution works.
In case that URL is broken in the future here is the solution:
Open the Registry Editor, navigate to:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Class
select key {4D36E965-E325-11CE-BFC1-08002BE10318} (now's a good time to backup)
delete the LowerFilters string value
delete the UpperFilters string value
Restart Windows.