Besides fighting games in general, I haven't found many arcade games to be my cup of tea. The only ones I really enjoy in freeplay-mode, is as of today Shinoby and Shadow Warrior. The reason for that is that in those two games, you get a real penalty when dieing and have to restart the whole level again, even if you have unlimited credits.
Other games especially beat'em ups tends to give you no penalty when dieing whatsoever as long as you have credits, thereby making them a walk in the park with unlimited credits.
I imagine this forum is full of MAME/arcade-enthusiasts that have great knowledge when it comes to recommended and not recommended games in this case, and I would love to hear your input.