Often you can save money on flights if you're prepared to take an indirect route. This is especially true of medium and long haul flights - and savings can sometimes be made on short haul flights too.
In addition to saving money, you can even see the stop over as a bonus because you get to see another place - if the stop over is long enough. Even just a few hours is normally enough to leave the airport and head into the city for a quick bite to eat, a visit to a museum or just a walk around to take in the atmosphere.
With Skyscanner you can easily compare direct and indirect flights to see which is cheapest.