(1) you can't afford to cover the loss if it should occur (or maintaining/raising cash to cover it would be more expensive than the cost of insurance);
(2) the peace of mind from knowing you won't have to worry about raising cash to cover a loss (even if you could cover it) is worth the cost of insurance to you, even if it's a bad deal financially; or
(3) you know more than the insurance actuaries about your individual risk profile and have an edge (which is rare but can happen -- e.g., you know a specific product model is extraordinarily likely to fail and buy a cheap extended warranty for it).
The first is the best and primary reason to buy insurance, the other two are corner cases.
Auto liability insurance is an example because it protects other drivers. Another example might be homeowner's insurance, which (if you have a loan) protects the lender too because the house is collateral.
Or back on amazon, under the different name