For video games alone, a lifetime. I have essentially complete ROM sets for everything through sixth generation consoles, and a wide variety of newer stuff (a full Wii set minus the obvious shovelware, a selection of the better PS3/Xbox 360 exclusives).
For movies, not quite as much. I'm mainly an emulation hoarder (who had to buy a bigger NAS because my ROMs were crowding out my family's music and video files), but we have 10-15TB of movies, TV and music laying around.