State Farm is one of the largest insurance companies in the United States, and two of its main competitors are GEICO and AETNA. GEICO is an acronym for Government Employees Insurance Company, and it is known for its low rates and online services. AETNA is a health insurance company that also offers life, disability, and long-term care insurance. Both GEICO and AETNA are large companies that offer competitive rates and services to their customers.