Once again, taxis are cheap and convenient and driving on your own is not recommended. But if you do insist, be careful. Drivers in Jordan are not bound by the rules of the road. Lanes are only recommendations here and the winding streets are difficult to navigate. Traffic congestion is often severe, made worse by the fact that there's no ring road for through traffic.
Driving in the city isn't too hazardous. While there are lots of fender benders, you don't drive fast enough to make things too dangerous. The countryside is another matter. Be extremely careful on the cliffside highways outside of Amman. Fatalities are commonplace.