It's wise to carry insurance if you drive, regardless of whether you own a car or rent one.
If you're renting a car, the rental company may offer you insurance on the spot. Rental car insurance is optional, but it's a good idea, particularly if your auto insurance policy doesn't extend to rented cars.
Don't mistake rental insurance for rental reimbursement. That's an add-on coverage that reimburses the cost of a rental if yours is totaled. If you find that your car insurance plan doesn't extend to rentals, it's worth purchasing rental car insurance.