With the economy in feefall and banks in serious trouble, would it be wise to withdraw all money from the bank before it fails?

As long as you have less than $250K in a single bank, and it's FDIC insured, then you don't have to worry. If you have more than $250K in cash, then simply spread it among several banks, each of which will be insured to $250K max.

The $250k insurance coverage is per person, per account type, per bank.

A joint account would provide $250K for each owner.

Regular accounts and IRA account are insured separately. $250K for each type.

Many other account types (such as a trust) are also insured separately.