All states have what are referred to as state guarantee funds.  Operated by departments of insurance, guarantee funds are insurance funds that receive contributions from carriers that operate in the state.

Guarantee funds are used to compensate annuity owners in the event that the insurance company becomes bankrupt or insolvent.  Funds are distributed to policyholders who purchased products from the insolvent company.

Levels of compensation vary by state, but annuities are typically insured up to $100,000 per contract.  In the unlikely event of multiple bankruptcies happening at the same time, the various contracts with different insurance companies would each receive compensation up to the statutory limit. 

Variable annuities—with the exception of the portion of funds that are allocated to the fixed account—are not insured by state guarantee funds.  

Check the website of your state department of insurance to understand what levels of compensation exist in your state.