Should A Refrigerator Run On Its Own Breaker?

Yes. Any major appliance or anything with at least a 1/2 hp motor should be on its own circuit. For example garbage disposals if at least 1/2 hp, garage door openers, dishwashers, etc. If its power consumption is at least 1500 watts @ 120 volts it will draw about 15 amps and should be on its own circuit. For example Space heaters, microwave ovens toaster ovens etc