Personal Accident/Injury insurance (PAI) is basically medical insurance—to pay doctors’ and hospital bills if you’re injured. It may also include compensation for such grisly possibilities as loss of limbs, eyes, ears, fingers, feet, etc.
Not a pleasant thought, but losing them and then running out of money because you’ve lost them is even worse.
On a happier note, you may already be covered for these perils. If you have doctors’ and hospital insurance at home, check with the company that insures you to see whether foreign travel is included in the coverage. It often is.
If you’re adequately covered, you can probably decline the PAI offered by car rental companies (which is what I do). A car rental company’s PAI may be secondary insurance, and thus wouldn’t even pay up until after other coverage is exhausted. If you’re already adequately covered by some other policy, why pay for PAI?
However, PAI is not the same as trip cancellation or medical evacuation insurance, which you may want to consider if you have a medical condition that may interrupt your trip.
USA: contact InsureMyTrip.com for no-obligation price quotes on all sorts of policies.