No-fault accidents appear on your driving record. If, for example, you were rear-ended by another driver in traffic, and your vehicle sustains damage, you need to inform your insurance company. When you do this, the company will take note of the accidents on your driving history as they consider your new car insurance rate. Whenever a claim is submitted, whether you’re at fault or another driver is, you can be sure the insurance company will record this on your driving record and use it to quote your rate even when you shop for new insurance.