In general, you should hook them all up. Just tie all like-rail wires together at the terminal on your power supply. Multiple wires are used to ensure low voltage drop across the lenghty cable, since high currents are drawn.
Your supply should have at the minimum a +5 and a +12 output. The -5 rail is not used by many boards, though Midway boards tend to use it. If your supply has the -5 rail, wire it up.
It is customary to take 2 or 3 of the higher numbered position ground wires (at the end opposite the key) and use them for ground returns on buttons. You should have, as an absolute minimum, 4 ground wires, 2 5V wires, and 1 12V wire. I tend to stick with 4-6 ground, 4 5V, 2 12V, and 1 -5V wire. The more wires you use, the more reliable things will be on modern, high power draw games.
The JAMMA board will again tie all like-rail contacts together, so which individual wires you choose does not particularly matter. Remember that any wire you don't hook up from a set will be "hot", though, and must be insulated to prevent inadvertent contact with ground.