My most common tools are nut drivers: one size for speed nuts, and another for the metal posts. Short needle nose pliers, and a phillips head and flat head screw driver, with the latter being absolutely necessary if working on Gottlieb games.
I have 2 soldering irons. One cheap one for coil lugs and diodes, and another for board work.
I've got both a rotary and vibratory tumbler, but I hardly use them. I prefer to buff things out. I tend to use my ultrasonic cleaner more, especially for star posts.
I've had a Dremel for a while, but never used it. Now with Nic's magic brush technique, it's been given a second lease on life!
Seshpilot hit the nail on the head though. This hobby has given me the confidence to attempt to repair all sorts of things.