Special note for 10.3.3 users: a driver change in 10.3.3 may cause some Firewire, USB, and RAID devices to no longer be able to mount that were in previous Mac OS X versions. The first reported problem has been fixed with 10.3.4. However, people not applying the combined update, and instead using Software Update to update to 10.3.4 and 10.3.5 appear to get similar symptoms. To get the combined update to 10.3.4, 10.3.5, and 10.3.6 repair permissions first through Applications -> Utilities -> Disk Utility -> select boot hard disk in Disk Utility -> click on First Aid, disconnect all third party peripherals (and dismount if necessary by dragging its icon to the trash), and check the links for the 10.3.4 combined (no longer available try 10.3.5 through 10.3.9, 10.3.7 combined update (10.3.6 is no longer available as a combo) depending on which software you are trying to reinstall. Repair permissions again after applying the update.
In some cases zapping the PRAM (hold the key sequence mentioned for four chimes) or resetting the NVRAM solves the inability to reach peripherals. Apple discusses this bug in more detail on article 107914. The other solution which was found on Apple discussions before Apple released the knowledgebase article 107914 is here:
Remove these files from the Hard Drive -> System -> Library -> Extensions directory:
detaching the hard drive from the computer or device and then booting back into Mac OS X may fix that problem.
Special thanks to the user Scoob on Apple's Discussions for finding this solution.
Has been moved to the Original Firewire Bug page. This describes the bug which affects at least 10.3.0 to 10.3.9 on all Firewire drives made with the Oxford chipsets 911 and 922, as well as a new problem with 10.3.6 through 10.3.9 affecting certain Initio and Part 2 chipsets.