Depends on the game...most raster games from the 70s to mid-to-late 90's plays identical to the arcade (save for the controls which is dependent on the game). Mame does VECTOR games OK with high-res displays (or awesomely if you build a Zektor Vector MAME cab).
For the most part, if the game you're thinking of doesn't have special controls, is a raster game, and doesn't use 3D graphics, you're looking at a pretty damn close comparison. If it DOES have 3d graphics, you still can get damn near identical to the real thing, but you're going to need horsepower under the hood.
SOME claim trackballs/spinners have a "lag". I claim their are smoking rock or haven't configured MAME properly or something because I am pretty sensitive to lag and I don't notice ANY lag.
It might not be lag but there are some issues w/ analog controls (specifically spinner and trackball games) and MAME regarding resolution etc. I spent a lot of time looking into this. For instance, I have a few Happ's trackballs and they in no way behave like the same ones in the arcade. Crystal Castles, Centipede, Tempest, etc.
I live close to Funspot and compare often. They just aren't the same IMO. I don't keep up to date w/ every MAME release so it may be better now. I think I'm running .110 or around there in my cab.
I agree with the rest though. Mame comes real close on raster games w/ a nice multi-sync arcade monitor. Vector games looked nice on my PC monitor w/ the artwork but that slow decay and bright dot is missing (Asteroids).
I think really everyone's idea of "how close to the real thing" is relative. Some folks play Robotron w/ Happ supers and enjoy it. I can't play it with anything but Wico 8 way leafs.
Same for Defender, I tried playing it with a 2 way micro-switch joystick. Doesn't feel right. Same w/ the position of the reverse button.
The again maybe I'm at the extreme end of the scale.

~telengard