Choosing a bank to place your money is not as easy as simply finding the one that is around the corner from your house. While the FDIC in the US guarantees deposits up to $250,000 per institution there are reasons to pick one that is well capitalized. Here are some of the best reasons:
If your bank fails; and there have been hundreds of bank failures in the aftermath of the great recession; it will be very inconvenient. It may be awhile (days to weeks) before your bank is switched over to the receiver bank or your money is returned to you by the FDIC.
If you have special privileges at your bank, like special CD Interest rates, or a great teaser rate on savings, and your bank fails; the FDIC may not honor those rates.
If you are dependent on a HELOC or a line of credit at a bank it is especially important you find a well capitalized bank. If your bank fails you may lose access to your credit. It is much better to bank at a strong bank where you have less risk of losing your line of credit.
While the likelihood of the FDIC faltering on its obligation to pay in the even of a failure is small, it is possible that a mega bank failure could place a large strain on the FDIC and Congress may not honor the FDIC line of credit.
One additional consideration is the possible loss of access for an extended period of time to your safe deposit boxes. You would eventually regain access, but it may not be at your convenience.
I've included a link to a bank ratings screener that you can use to see if your bank or potential bank is safe.
select one here...