What happens if I (a US citizen) rent a car in, say, the UK, and crash it because I was driving on the wrong side of the road? Do I have to pay the damages out of pocket? What if I don't have the money? Will my US insurance carrier cover the damages?
You are fully liable for any damage you do to a rental car, and in most cases also for damage that others do if you cannot establish that they are to blame. I cannot comment on country or company specific practices but I'd be surprised if this did not apply in the vast majority of cases.
If your travel insurance covers car damage that may be an option. Most travel insurance packages do not do so as standard. I have never seen one which does.
ALL car hire companies offer insurance.
This usually comes at several levels.
The basic level may have a very high "excess" - I've seen $1000 to $3000 quoted. This means that you are liable for "minor" damage but covered for a more major accident.
You can usually get "sensible excesses" - say $500.
And most offer a complete waiver option where you pay nothing for damage.
Read the fine print !!!! I have seen companies that do not cover eg rear end damage or underbody damage in their insurance - ie if you back into something or drive over a small wall or large rock (and I've managed to damage my own vehicle both ways in my lifetime) then you would not be covered.
Your main insurance company at home MAY be prepared to sell you hire vehicle insurance. If you have not arranged this in advance assume that you are not covered. It's almost certain that you will not be.
Not having insurance or having a very large excess is a gamble.
I almost always pay for maximum cover and have never damage a rental car.
Be wary of any company that does NOT offer insurance when you hire a car. Having their old bomb replaced with a newer one may be attractive.
I always photograph the whole exterior of a car extensively when hiring it. I make sure that the photos show all dents, scratches, bumps etc. The company will have a form to fill in initially where you and they mark in any existing damage but they are usually much more casual about this than you should be.
... because I was driving on the wrong side of the road ...
Crossing to the wrong side of the road and having an accident is a real risk.
I'm in NZ - only 4 million population.
We drive on the left.
Every year we have on average several accidents with usually multiple deaths where tourists accidentally crossed the centre line and collided head on with another vehicle. While circumstances vary and an accident may be for other reasons, the majority of these do seem to be due to left/right confusion. The percentages are not vast, but it does happen.
10 years ago my wife and I and a friend spent 6 weeks in the US and in Europe, driving long distances on many days. I mainly sat at a window and took photos and my friend did maybe 70% of the driving. He is an excellent driver, very experienced and capable in tricky situations. In our country he probably often drives faster than many but does not have accidents. He was incapable of completely adjusting to the left/right change. While we did not have many incidents and while we corrected him promptly (as one does :-)) it would not be uncommon to have him make interesting intersection calls. Not a vast number but enough to be of concern. Most people come back alive. Take due care, THINK ahead. Get the feel of how to handle driving into a divided roadway at an intersection - harder than you may expect under pressure.