It depends. There are 3 ways to install Panther (search the forums here for more in depth info about each method):
1) Upgrade- This will update your MacOS to the newer version, leaving all apps, preferences, documents, etc. intact.
2) Archive & Install- This will install a fresh copy of Panther and will leave all of your apps and documents, etc. intact. It will also preserve most, but not necessarily all, of your preferences. It will save a "Previous System" folder containing those prefs and such that did not carry over. You can manually move the ones you want to keep, and you can delete what's left after you're sure everything's running OK.
3) Erase & Install- This will erase EVERYTHING on your hard drive and will install Panther and it's included apps (Safari, iTunes, etc).
So, 1 and 2 will keep all your stuff safe. Either way, it's a good idea to always keep backups of your important files.