Now what? You could find out how your bank is doing by reviewing the Uniform Bank Performance Reports (published by the FDIC) or reading an analyst report (but we remember the recent credit crisis and the limited value that should be placed on analyst ratings). Unfortunately banks' regulatory ratings are not public but if the banks are in real trouble you can generally find Formal Agreements, Memos of Understanding and other similar communication published on the regulatory websites (FDIC.gov, OCC.gov, etc).
If you think "better be safe than sorry" and would like an alternative, a safety net can be a CDARS program. This program is offered only by some banks; it allows up to $50,000,000 (fifty million -- but the coverage may be different depending on availability) FDIC insurance coverage through member banks swap of deposit money. The rates on these deposits are generally lower than the general CD rates at the banks because the banks have to pay a spread (a small fee) to the administrator.
You can secure your money in the bank! CDARS can provide significantly more FDIC coverage for your money. To find a bank in your area that participates in this program visit CDARS.