We always rent a car where ever we go, and I must say that driving in Puerto Rico was one of the scariest places we have driven (we've been to Ireland and driving on the left hand side of the road in the right side of the car and using a stick with the left hand along the little tiny walled roads was not as stressful as our drives in Puerto Rico).
The major roads were no problems at all, except for the funeral that we got behind so all the cars were stacked up behind all the people walking to the cemetery and then everyone was cutting through the gas station, so that took a little while, but the worst part was in the interior of the country.
We drove from the rio grande area to the other side of the island to go explore, and we didn't find anything very interesting to stop at, and whenever we tried to get down to the water, we had trouble finding access, but the absolute worst part was our drive back. We took the highway through the interior and then cut through some back roads to get back to our hotel. Many of the roads ran through or along the edge of the rainforest. They were very winding and narrow. I don't know how many times I thought we were going to have a head on collision. The people there drive extremely fast around the curves, and if we had been driving at the same speed, there were a few times that we definitely would have crashed, as there would not been enough time for both vehicles to stop.
By the time we got back to the hotel, I was sick to my stomach and shaking a bit. Did not like driving on those roads at all. If you do rent a car, just be careful of where you drive. Stick to the main road if possible, and you should be fine.