Only deposit accounts at federally insured depository institutions are protected by the FDIC. Check to see if your bank falls into this category. In general, the government will protect accounts up to $250,000. If you have an account with special ownership, such as a trust, or an account with co-owners, this may change the amount of coverage you receive.
If you invest in an annuity or mutual fund with the institution these are usually not protected by the FDIC.