Not sure of an actual average, but I would wager around 3 feet. I know in the Project Arcade book, the height from the base to the bottom of the control panel box is listed at 33 inches. And then it's probably another 3-4 inches or so to the top of the CP.
But rather than picking a number based on other arcade cabinets, I'd build something that works for you. After all, if you're primarily using it, you should make something that is comfortable for yourself.