I think what you're looking for is what's called a Dual-Position Double Throw (DPDT) relay. It provides two positions (completes two circuits, one or the other) and has a double throw action. What this means is that when you apply power once, the relay flips to one side, which in this case, could be left open, thereby cutting the circuit. When you apply power again, it throws to the other side, completing the circuit you want to apply power to.
Placing a on/off pushbutton on a single throw relay means that in order to keep power going through the circuit, you have to keep power in the relay, and that's not a good thing for the relay. The coil will burn out after a short while that way.
Best place ever for answers to questions like these:
HowStuffWorks : Relays