Lawn care services will typically mow weekly or bi-weekly. Some will do on call, but that usually costs more due to scheduling and most often these are the people that let the grass get out of control before calling. Typically, your grass will always look best right after it is cut. Maybe not the greenest or most lush looking, but at least the blades are all the same high and the turf is level. Like Bert said, there are some differences between when to mow based on the turf type, climate and cut height. If you are not familiar with the 1/3 rule, basically you never want to cut off more than 1/3 of the blades. So if your climate and grass type allows for and looks good at 3", you will never want to let it get to be more than 4.5" tall before you cut. Following this rule, cutting shorter will require more often mowing as it will take less time for the grass to grow that 1/3 that needs to be cut off. I live in SE Michigan and have Kentucky Bluegrass and Annual Ryegrass. At a 4" height of cut, I am mowing my back yard every 3 days right now. The front yard I cut at 3" but am able to cut at the same time as it does not grow as fast, nor is the turf as lush. When the warmer months come, July or August, I can go 5-7 days inbetween mowing.
Lastly, if you have the time and physical capabilities, mowing your own lawn is not only the most economical but also the most rewarding. You have greater control of when and how it is cut, not to mention the added benefit of exercise. I have never had a professional lawn care service, but I can imagine that for what a years worth of service would cost you could buy a high end residential self-propelled mower that would give you many years of service and pay dividends in year two. If in the end you must rely on a lawn service, just ask them questions like Rivets said. They are performing a service, and thus that service must be to your satisfaction, both in how they treat you, but how they treat your lawn!