Media Player
The only reason I wanted an exploited box was to run media player. So I could watch all my DivXs and cool stuff I have downloaded, shame DVD support is shocking, but thats another topic. In short, the media player in my opinion is the single best reason to get your box exploited.
Booting 'Backups'
I didnt even think about playing copied games, personally I think having the option to play "Backups" makes you end up with a bunch of games you dont really want to play. I much prefer shelling out for a real game, finnishing it and then maybe even swapping it at my gamestore for a new game. In my opionion if you wanna play copied games, you should get a chip.
Emulation and Homebrew
Emulation was something I thought would be very cool, My Dreamcast was the king of emulation, but the xbox has so many cool things like the N64 emu thats just as good as a REAL N64! However, I dont find myself booting them much. Maybe one day.
Other
Other things are cool, like being able to copy games to the HD, but I still have the stock HD so thats no good for me.