I would never work a single day without my own coverage. My father, a physician, advised me 'waaay back when I was in nursing school to never trust an employer to look out for my interests and never work without my own coverage, and everything I've seen over the last 25+ years in nursing has only reinforced to me what excellent advice that was.
NSO and Marsh Proliability are the two companies that get mentioned most often in these discussions, and specialize in liability coverage for nurses and other specific health occupations. I have had coverage with both at different times over the years, but (knock on wood!) have never had to use them, so I have no opinions or preference for one over the other. People here have also mentioned having coverage as a rider on their homeowner's policy, but I have no idea how that would work and prefer to deal with a company that specializes in liability coverage for nurses.
As JustBeachy noted, the NSO and Marsh policies include not only coverage if you're sued for malpractice (which is statistically unlikely for nurses), but also provide coverage for legal representation if you have to go before the BON for any reason, and if you're deposed or called as a witness in a suit against someone else. Both those situations are much more likely to occur over the course of a nursing career than getting sued, yourself, for malpractice, you would certainly want to have (your own) legal representation in either situation, and paying for your own attorney out of pocket in either situation would cost more for the first hour than the typical annual premium for the insurance.
Also, your employer's insurance only covers you while you're at work for that employer. Your own coverage covers you 24/7 anywhere you go -- if you choose to volunteer in some nursing capacity, if you choose to help a relative or neighbor with healthcare needs, if you stop to help someone in an emergency in public, etc.