Any and all measures of wealth (dollars, Euros, gold coins, bearer bonds, stocks, etc.) that isn't Practical Currency are susceptable to this. For the most part, money is only useful to trade for something of value to you (e.g., food) — you can't physically eat a dollar bill and physically get nutrients from it. The one you are purchasing from, in turn, will only accept your money if he believes he himself can turn around and get something useful for himself for it. In a relatively normal and stable free-trade environment (as in you are free to trade with others if you want), money is very useful, as it bypasses the highly inefficent bartering system and needing to construct a complicated Chain of Deals to get what you need or want. The truly dire life-or-death situations that bring this trope into being also removes the "relatively normal and stable free-trade environment" requirement. (Depending on specifics, you could end up in a Money to Burn situation, but again, that's not exactly a normal circumstance.)
Fiat currency ("fiat" meaning "because I (i.e., the government) say so") is the most vulnerable kind of money to this trope in fiction (as in "most likely to be rendered powerless"), as it is money backed by nothing but the full faith and credit of the government. The US dollar used to be redeemable for gold at a fixed price until the 1971 Nixon Shock, when Richard Nixon unilaterally took the US off the gold standard in order to pay for the mounting expenses of The Vietnam War. You can still purchase gold on commodities exchanges, but you can no longer go to a bank and force it to take your dollars and give you gold (actual coins made of gold were confiscated back in 1933 by executive order signed by FDR). At the very minimum, because Federal Reserve Notes are considered legal tender in the United States, the US dollar will always be useful for, as it is printed on them, settling "all debts public and private" — in the US, this means you can always repay a debt you owe to someone else with US dollars, even in pennies if you want to be a jerk.note This includes the taxes you incur every year, so if nothing else the US currency in your wallet is useful for keeping the Internal Revenue Service off your back. However, if you take away the government via a big enough catastrophe, this usefulness evaporates because both the legal enforcement infrastructure (e.g., the court that would have your debt cancelled if the one holding your debt tried to refuse your dollars) and the most basic need it could satisfy (i.e., the payment of your taxes to the IRS) disappear.
Measures of wealth that derive from currency such as stocks and bonds are more vulnerable to sudden worthlessness, but in most cases the catastrophe is limited to the world of finance. The general public generally doesn't see the effects of such semi-frequent events beyond the news, at least not in an immediate "Oh my God, the world is ending!" way with a clear cause-and-effect relationship conducive to a two-hour movie. Then again, in fiction not based in the world of multinational corporations and international finance, who but a (particularly stupid) Corrupt Corporate Executive would even deign to try to go "Screw The Rules, I Have Stock Options"?
Going the other direction, commonly-traded commodities like gold are frequently sought by those who suddenly have lost faith in the usual stores of wealth (e.g., have fled the stock market) — see the recent financial crisis and the skyrocketing of the price of gold around the same time. However, for the kinds of life-threatening widespread disasters that call this trope in, gold falls victim just as much as cash. Gold lying around isn't going to be as common as it once was (see two paragraphs up), but even in times when gold was the standard medium of exchange, it's still really heavy and inedible. Hoarding gold implies that the situation is bad enough to wreck the utility of government-backed legal tender but not so bad as to be unable to find others with resources you want so that you can trade something of otherwise little inherent utility for those resources — life-threatening situations are past that point.
In the absence of any rule of law, such as in a dictatorship or civil war, the greatest power is the one holding the biggest club who can just confiscate money and other assets on the merest whim.
