I need to wire an old air compressor into an existing circuit breaker box. I don't know if this should be done, or do I run a plug in for it?

It is always easier to connect this with a plug-in connector. That leaves you free from a lot of wiring requirements.

Actually, using a receptacle for this doesn't free you from as many requirements as it adds. Things like box fill, using the correct receptacle, grounding the box if it's metallic, all come into play. That said, it's really a better idea for a few reasons.

1. You can easily use the receptacle for other equipment you may acquire in the future.
2. It's easier to take the compressor with you if you move.
3. It's easier to extend or move the circuit later if you decide the compressor should go somewhere else.
4. It serves as the required disconnecting means.