You can get a system that runs everything that's
currently playable in MAME (including the benchmark games like NFL Blitz) in a mini-ITX system these days, but you'll probably want to build it yourself. I built one here:
http://forum.arcadecontrols.com/index.php/topic,129277.0.html There are pictures further down the thread too. Obviously, you're not going to use the m350 case if you're going to use a discreet GPU...
As I understand it, you don't necessarily need an AVGA anymore, as long as you've got a GPU that supports an app called Soft15khz. I'm not much of a help here, except to say that the Intel HD series of integrated graphics (i.e. Sandy Bridge and Ivy Bridge chips) do NOT currently support Soft15khz.
Alternatively, if you want to get
really small but don't want to build your own, take a look at the Intel NUC, or the Core-based systems made by Giada PC. Again, harder to get output to an arcade monitor, but almost impossible to get that kind of power in a smaller device.