Is there any truth to the rumors about arcade games with free game backdoors?

I never seen confirmation that any of those rumors about codes were true. There is a setting called "Free Play" on most arcades that the owner can enable, however, which involves opening the case itself. This may have been what started the rumors.

EDIT: That's not to say that some games didn't have a glitch that allowed free play to become available without opening the cabinet. This sometimes involved actions like physically turning the machine off, then rebooting it again when it was at a certain point in the startup sequence.

I can't speak for any other titles, but "A certain version number" of Mortal Kombat 3 did have a code, You beat the game, then did a series of button presses and joystiq movements as the credits rolled" and you would get infinite credits upon the game reloading. This of course infuriated arcade owners to the point that an update was patched in to remove it. Luckily, my arcade never did update all the MK3 machines it had. But Yes, at one point, stuff like this did happen.

Tempest had a bug that gave you 40 credits if you ended the game with a certain score. They fixed it later on, so it only happens in rev1 rom.

http://www.arcade-museum.com/game_detail.php?game_id=10065

There are probably other examples out there.

Another one I forgot about is the "Konami Code":

http://en.wikipedia.org/wiki/List_of_Konami_code_games

In some games it grants full powerups, but in others (like Contra) it gives additional lives.