Not that I have it but most banks only secure amounts up to $100k so if you put $1M in there are you at risk of losing $900k if that bank shuts down? How do people store large sums of money, do they spread it out in $100k chunks?
It depends on your situation. For families with small amounts over the FDIC limit, there's account structures that let you get multiple coverages. Things like holding 100k in an account in joint with your wife, each of you holding 100k in individual accounts etc.
For larger sums and institutions, there's CDARS. This system spreads your money out to multiple institutions with an eye to FDIC insurance limits. Some people feel this system is abusing FDIC, so I suppose it's possible it gets outlawed / shut down some day.
Alternatively, you can just invest it yourself. Treasury Direct allows small buyers to buy US govt bonds at finished auction rates, or submit a qualified bid at auction. You won't get great rates, but Treasuries are about as good as dollars.
You can store millions of dollars in deposit accounts, you just lose the explicit FDIC guarantee. So you look for rock-solid banks. Bankrate.com has "Safe and Sound Ratings" that show the relative strength of various banks. You put your excess deposits in those banks, and you are pretty safe.
Note that in addition to the explicit FDIC guarantee, there is now an implicit guarantee that certain institutions have been deemed too "big to fail", and will be backed by the full faith and credit of the US Government, without regard to the capitalization of the bank. Bank of America, for example, is not well capitalized and is carrying billions of dollars of "assets" that have little or no value. Yet government policy keeps the bank afloat and your deposits secure.
Another strategy is to use municipal money market accounts, which provide secure (but not guaranteed) deposit-like accounts as well as a tax benefit.
If you have > $1M in liquid assets, you probably need a financial professional and attorney advising you to make sure that you are aware of and are controlling for risk in a way consistent with your longer-term goals.
If you want to store that much money, find a good hiding place.
(E-mail me the location. I'll keep it a secret. I promise!)
But I think instead you want to invest that much money, in a cash-like liquid form.
You can do $250,000 in a bank (beyond 2012) and then spread the rest over some big-name brokerages with money market accounts.
But, as JohnFx pointed out, with that much cash you can do amazing things with it. Think bigger.
A better answer is to put the money in a Dodd-Frank qualified non interest bearing checking account. FDIC covers the entire balance, there is no upper limit on the insurance. This will only be good till the end of 2012 but for short term landing spot this works well. Forget the interest you will earn and go for the safety of the principal.