For non-power applications (I/O such as controls, mostly), just about anything will suffice, but 22AWG seems to be what most arcade manufacturers used. It's small enough to fit into most connector systems, but big enough that it has some "body" and resists mild physical abuse that the underside of controls panels sometimes sees (due to it being lifted occasionally to access broken switches, buttons, and often the monitor remote).
24AWG can also be used quite fine with some caveats. Normal network cable is solid (and also sometimes 26AWG), which has some problems with crimping into most connector systems including common terminals. Solid wire is also more apt to break when flexed. Electrically, there's no real problem with 24-28AWG. 30AWG is also likely fine electrically, though over long distances even a few mA like that seen on a conventional 5V arcade I/O circuit can start to cause problems on such tiny wire.
28AWG and smaller are likely too brittle for most purposes. Solid especially will pretty much snap the instant you bend it too much. 26AWG and smaller also may not secure into the terminal blocks on your IPAC very well.