As a general rule, rental cars are exceptionally well-maintained and rarely break down. It just makes good business sense for the rental car companies to keep their vehicles in perfect working order, because they can’t rent a car that is not running and it always makes for a bad customer experience if a car breaks down. So the rental car companies are diligent about maintenance and oil changes, probably much more than you are with your own car (how many times have you gone beyond the recommended mileage an oil change?). Even so, breakdowns do occasionally happen, either for mechanical reasons or just a blown tire caused by an unavoidable object on the road.
It can be a scary experience to have a breakdown in an unfamiliar area, so it pays to do a little advance thinking. Many rental cars now have a 24-hour toll-free roadside assistance number printed right on the vehicle, either on the driver side window or sometimes on the windshield corner. You might also find it on the rental car contract or jacket that it comes in. Either way, it’s a good idea to check for the number when you pick up the car, and if it’s not printed right on the car, go ahead and save it in your phone just in case. You’ll probably never need it, but if you do then you’ll be glad that you have it.