No (however, a backup is a good idea anyways, never know what may happen)
There are 3 install choices, 2 of which keep all your data/apps intact:
Upgrade: Overwrites Tiger with Leopard, keeps all data/apps intact
Archive & Install: Achives your system and library folders, then installs Leopard over Tiger, apps/docs intact.
Erase & Install: Wipes hard drive, installs Leopard. apps/docs not intact.