I bought an xbox specifically so I could play emulators like Mame etc on my big tv - and I havent been disappointed..
There are two Mame projects on it by Mameox is the best and is up to date with the latest 0.79 build.
However, Mame is a bit memory hungry and with the limited memory that the xbox has means some of the larger (mainly Neogeo) games wont run. However most of the games run fine and its great fun to be able to play four player ninja Turtles / Gauntlet etc.. on it.
For games that Mame cant load you will need the port of Winkawaks (Called KawaksX on the xbox) - It plays all Neogo games and CPS2 games very well.
Of course there are lots of other emulators too ... c64/nes/snes/gba/megadrive - anything you can think of really. After all its really just a PC in a box.
My mate even has the xbox keyboard from Datel so he can play the c64 text adventure games properly..
Emulator Im most impressed with though has to be PCSXbox - a playstation emulator that plays most of my favourite games fine although its not quite full speed on some games