While in general, I am too young and from a region without big gaming arcades back in the time (at least to my knowledge), there were some placed at the ice skating rink of my hometown, presumably many years after their original releases. While there where several ones (one must have been Michael Jackson's Moonwalker), the one that got stuck most in my memory was Out Run, a racing game with the objective to finish a course using a sport scar versus a strict timer.
I do not remember if I just watched others back then or how I fared back then if I tried. But as nowadays you can just play it online, for example on archive.org via streamed arcade emulator, I gave it another run. I could not even finish the first level. Arcade games were serious business, that would not go easy on you (as they wanted your money and where often quite short, this is not even surprising).
Apart from the ice rink, I remember a gaming arcade at the holiday resort in Croatia my family visited several times. There, I saw Ghosts n' Goblins for the first time! I also do remember one other game about a bald guy with a naginata and other Japanese weapons that I have not identified so far. If anyone has a clue of what game I am talking about, I would be really happy if you comment on it.