If you know someone with an already-modded XBox, they can create the tools to do what's called a TSOP Mod through the use of one of the 007 or MechAssault games and a corrupted save file. This is a great method, as it fully emulates a hardware-modded XBox, with no hardware to install (save for one wire added to the motherboard). I've done this method to three or four XBoxes now, and it works perfectly.
MAME runs well, I'm running the MAMEOX build. Neo Geo and some CPS-2 games suffer a bit (internal RAM limits of the XBox), but there is an execellent emulator called FBA-XXX that runs these like a champ.
You can also get RAM upgrades for your XBox, but they are a pain to install (surface mount) and the installation services are very expensive IMHO.
Also, there are some excellent controllers to "padhack" and create "real arcade" sticks for the XBox. This takes you that last-step into real arcade. Combine a true arcade controller with a nice big LCD panel, and you are in arcade nirvana without leaving your favorite chair.
Edit: Forgot that the TSOP Mod is dependent on the version of XBox that you have. The best ones are the older ones (v1.0 and v1.1), as they had a larger internal BIOS Flash chip.
Edit 2: An excellent place to get started:
http://www.xbox-linux.org/wiki/Getting_Started . Also, if you search for XBox Linux, there tends to be a little more info openly available, as it's not the grey-area that emulation is.