Well, generally it shouldn't be necessary, but "shouldn't" and "isn't" aren't the same. If it's acting that oddly, it's probably worth at least a reinstall to see if that helps.
First, I'm assuming that you have a retail copy of Tiger. If you're still using the version of 10.3 that came with it, the suggestions are basically the same, though. (If you are on 10.3, an upgrade might be a good idea, though you may do better to wait a couple months until 10.5 ships.)
So, the easiest thing to do is an archive and install; boot from the OS install disc, then select install, and under options make sure "archive and install (preserving Users)" is set. What this will do is install a fresh copy of the OS, but bring over most of your applications and all of your user settings. This gives most of the benefits of a clean install without a lot of the hassle.
Once that's done, reinstall any applications that didn't make the transition (you may want to just reinstall everything to be careful, since it shouldn't take that long), and while you're at it make sure everything is the latest version available. If you're happy that everything is ok, delete the "Previous Systems" folder at the top level of your boot drive.
If you want to do a completely clean install, you're going to need a way to backup everything you want to save; my suggestion would be thus:
Get a backup drive, then use Carbon Copy Cloner to clone your boot drive to it. Check to make sure the clone operation worked properly (boot from the backup, that is). Then boot from the OS disc without the backup drive installed, reformat the hard disk, and install a fresh copy of the OS.
Then when you start up, use the neat little transition application to import your user data from the backup drive--this works quite well in my experience. Once that's done, immediately update to the latest OS version and anything else Software Update suggests. Finally, install all your applications (and again, make sure they're the latest version).
The drastic reinstall may not be necessary unless you have a BUNCH of junk on your boot drive, or perhaps a whole lot of large files that have severely fragmented it...