Any type of martial arts training benefits greatly from core strength training, aerobic fitness, and flexibility. Additionally, anything that increases balance and overall coordination is helpful. Boxers do circuit training, speed and heavy bags, and jump rope, in addition to road work. You could do worse than to emulate them. Personally, I avoid heavy impact training to my knees, so I no longer run. I do like elliptical machines, though. In fact, I need to get back to that soon.
In my opinion, the kind of power that a stand up fighter needs is explosive power generated from a strong core and back, shoulders and legs. Aerobic training helps with the wind, so that kind of power expenditure can be maintained for briefs periods of time without becoming gassed.