What can happen to your car if you run over a traffic cone?

Answer 1

It would be extremely unlikely for any permanent damage to be done. Traffic cones are made on purpose not to hurt cars if they get run over.

Not really true - I was travelling about 60 mph late at night one day and discovered a traffic cone lying sideways in the middle of the highway. For some reason, I thought I had enough undertow to run over it (not!) - next thing I know - there's this loud scary "wham" and from then on I have this funny buzzing sound in my car that turns off and on. Worse, the cone broke my engine mount and caused a rather noticable dent in the underpart of my Honda Civic. Costly - am checking out how much to repair. I think that it shifted my hood as well as it is not aligned correctly anymore....