According to the latest PAP-98 (Personal Auto Policy, I hope I have the year right) which is the generic, established, form policy which most insurers use, not only are you covered while driving other people’s cars, but they are covered driving yours as long as it was done so with your permission (not stolen). In this sense the policy covers both you and your car. Now if your friend has a PAP and she wrecks your car, generally her insurance would pay out. If she was not insured and rarely used the vehicle (a couple of times on a road-trip for instance) then your policy would cover the accident. In either case the car would be covered.
Not all insurers use the PAP-98, and many insurers include endorsements which may alter this clause, so it is best to read through your policy first and make sure that it covers your car in someone else’s care. Also some states have certain requirements which might alter this general rule, but they are the minority.
If this person was going to be regularly using the vehicle and does not have insurance of their own, then your insurance company is going to want to add them to the policy as a driver, mostly for the sake of rating the policy correctly. If your insurer finds out that your live-in girlfriend takes your car to work and does not have insurance, they’re gonna be pretty irritated and may cancel your policy, so it is best to be honest. If she’s got a clean record it probably won’t increase your premium at all.
The bottom line is to read through your policy, especially the definitions section which describes “the insured” and “your covered auto”. It should explicitly spell out who and what is covered when.