Here's a few links to help you evaluate the relative safety of you current bank and
a) get really nervous about your money's solvency, or
b) find the current (disclosed) status of a banking alternative.
and within that site, a great tool that's a little hard to find: safe and sound ratings:
The problem with FDIC is that they don't disclose ratings so you have no way of knowing who's on death watch until the funeral.
Bauer and Ambest charge for detailed reports, but basic rating analysis is free.
Bankrate also has a menu of other great financial planning and analysis tools on the site, all free.