Is it possible that I could have a 240V circuit with no circuit breaker?
If there's no main breaker, then there is probably another breaker box somewhere, possibly in the same enclosure as the meter.

Also, it's possible that the panel you are looking at does not have a main breaker at the top; it could be one of the breakers mixed in with the branch circuit breakers. If you can, post a picture of your breaker panel with the cover removed so we can see the wiring inside.