Unfortunately, there is no clear-cut answer to this question since repair policies vary between car rental companies. Not only that, but repair policies can even vary between franchises within the same parent company since each franchise is owned by a different person.
In most cases, customers are responsible for roadside assistance costs. That means that if you break down on the side of the road and need to have the car towed or have a new tire put on, you typically have to pay those expenses out of pocket. Also, if you blow out a tire or get a cracked windshield, you may also have to pay to replace those items yourself. 
There have even been reports online of car rental agencies making customers pay for repairs that are far more serious -- and expensive. For instance, one person claims to have been billed $1,500 after the transmission went out on the rental car that he was driving. 
Whether or not all of these stories are true is hard to say since people can post whatever they want on the Internet. However, it is worth keeping in mind when you rent a car. You should always read the fine print of your rental agreement to determine what is and isn't covered. Many rental agencies offer additional insurance that you can take out. However, you may find that your own insurance or the credit card that you use to rent the car offer similar coverage options. If so, you can save the money on the insurance. Memberships such as AAA can also be beneficial since they would cover any towing or roadside assistance services that were necessary even if you were in a rental car. 
Finally, always thoroughly inspect your vehicle before you get too far from the rental agency. Walk around the vehicle and check for signs of damage. If you do find damage, snap a few photos of it to document it. Don't forget to look at the interior of the vehicle as well. If the car sounds funny when you start it, or if any warning lights come on, return to the rental agency and ask for a replacement. Likewise, if you get a little ways down the road and notice that it isn't accelerating like it should or appears to be having other mechanical problems, it is well worth turning around and taking it back to the rental agency to get a replacement vehicle.