I live in the Bay Area, California. I had to take comprehensive (Liability and Collision) insurance and pay around $500 for six months until I paid off the debt. I recollect that I was required to take comprehensive if I have a loan on my car. Now that I have paid off the loan, how can I change my insurance to bring down the cost while maintaining the required coverage only?
If -- with your existing resources -- you can repair/replace the car after a collision, or non-collision incident (fire, vandalism or falling tree or hail, etc) then by all means cancel comp & collision.
If, on the other hand, you can't repair or replace it with your existing resources then definitely keep comp & collision until the car loses enough value that you can replace it.
EDIT: another alternative is to raise your deductible. That'll reduce your premiums.
If you don't have a loan on your car, you are not obligated to buy comprehensive or collision coverage.
But if you drop the coverage, you risk having to pay for any damage that occurs (or replace your vehicle) out of pocket.
An added benefit of buying insurance is that if someone else damages your car when you have insurance, the insurance company will do most of the work of collecting payment from the other party, saving you a lot of trouble.
Now that I cleared the loan, how can I change my insurance to bring down the cost while maintaining the required coverage only?
Call your agent (or call agents for several companies to get competitive quotes) and ask for a quote on the coverage you want. Then tell them to change your policy or cancel the old policy and start a new one at a new company.