The FDIC was formed in response to the bank failures of the Great Depression (no, not this one, the one in 1929), Prozac for the banking system so to speak. I think it was a mistake because one artifact of safety nets such as the FDIC is that those with moral weakness (aka "humans") might tend to take more risks than they would in the absence of the insurance.
For example, imagine a football game with no referees. Instead there is just Game Insurance so that whichever team loses the game actually gets to win. Both teams win! Cheating & incompetence don't matter! How hard would either team try if that were the case?? I would prefer strict rules strictly enforced, with real penalties, which is how football is conducted now. Anybody know of a Wall Street banker who has been jailed since 2008? I don't. Where are the hundreds of heads that should be rolling from AIG, Lehman, & Countrywide, to name a few? The only things that are rolling are their companies' executives . . . in cash. Win win.
But back to the topic, the FDIC is indeed an important safety net for those of us here at the bottom of the food chain. And a married couple can easily enjoy a million dollars of protection. At the same bank. Each may have an IRA and an savings account insured up to $250k per account.
Having said that, keep in mind that there is no risk-free investment or savings vehicle. Let me say that another way. There is no risk-free investment or savings vehicle. (Do a google search for "financial risk" to review the different types of risk.) This is important enough to say a third way: There is no risk-free investment or savings vehicle. Here's why.
Although CDs and bank accounts are FDIC insured, they guarantee that you'll be subject to inflation certainty. Not inflation risk ("risk" is when you're unsure whether or not an event will occur.), inflation certainty because inflation will certainly exceed the returns your bank can offer.
So ultimately, the types of financial risk you need to minimize depend on what order you rank the four main financial priorities for a portfolio: