Finally, it's a perfect fit if your local airport is crazy expensive, and you often have to drive to a larger, more unpleasant airport to save money. The prime example: Orange County. Nonstops from LAX to New York aren’t too bad, but if you live in Orange County and want a nonstop from John Wayne to NYC, it'll run you a staggering $740. However, book a flight from Orange County to Richmond, VA and connect through Newark, and your flight's only $202.
Who it doesn't work for
Because airlines love to make your life difficult, it won't really work for round-trip tickets: if you skip your connection on the way there, and never get on another flight, your whole itinerary is canceled. Airlines are real peaches like that. To take full advantage, you'll need to buy one-way tickets.
Also, if you live in a big hub city (Chicago, Dallas, Houston, everywhere else you see people sleeping on airport floors) and have regular nonstops everywhere, you're not finding many deals flying out. Though you might find some good ones coming home.
Likewise, if you're looking to fly a highly popular route, like New York to Miami or LA to San Francisco, airlines already have cheap nonstops on those routes. There just isn't much to save. Also true if you're going BETWEEN hub cities, so Chicago to Dallas won't have much in the way of bargains.