There are two basic types of life insurance: Term and Permanent.
Term insurance offers coverage for 5, 10, 15 or 20 years for people over 60, but the longest term available will depend on your age.
Permanent insurance provides lifetime protection for as long as you live, and builds some cash value inside the policy over time - but it costs up to 5 to 10 times more than term life for the same amount of insurance.
The cheapest life insurance for people over 60 would be a term life insurance policy for the lowest "term" (duration) of coverage, which would be either 5 or 10 years.
You may save some money on your policy by comparing pricing from several insurers, and choosing to pay your premiums once per year (annually), instead of monthly or quarterly.
Here's how to get free life insurance quotes for people over 60 years old.