Those penny arcades were great though. Nothing better than a roll of quarters and sneaking a pint of Jack into the arcade with your friends on a Friday night.
Lest we divert.......... You can open an "arcade" but there are strict laws governing the location such as near a school or church, and there is a limit to the number of machines you can have without obtaining a special license. Check with your local laws for the specific restrictions. Also, as IAAL pointed out, there are requirements for licensing use of registered/copyrighted material, so you would also need licensing from the manufacturers of the games you might want to use.
Keep in mind though that with all of the gaming options out there at such cheap prices, most consumers are buying for home use. A gaming arcade might not be too feasible. 20 years ago, you would have been rolling in quarters though.