The dollar’s sharp turn weaker into the end of the year is threatening to reshuffle winners and losers in global trade amid the toughest economic conditions in decades.

For countries like Japan and Germany, it is a source of anxiety, since a stronger currency makes exports less competitive as global demand shrinks. For the U.S., it is a more welcome development and might also help counteract declining prices. In some emerging markets, a weaker dollar is a relief for companies that must pay debts denominated in dollars.

Still, in today’s environment, few countries want to be the last one standing with a strong currency. Some economists worry that countries could actively seek to weaken their currencies in an effort to gain an advantage over their trading partners, setting off a round of devaluations that ultimately damage world trade.

Until recently, the dollar was one of the most robust currencies around, surging against everything except the Japanese yen. But in recent weeks — and particularly after the Federal Reserve slashed a key interest-rate target to near zero — the dollar has abruptly changed course.

On Friday, the dollar slipped against the euro, with one euro buying $1.406 late in New York. The dollar has weakened about 10% versus the euro and 8% against the yen since the start of November.

That is good news for U.S. exporters, but it is raising concerns in places like Japan and Germany, which are both gripped by recession.

In Japan, officials are so concerned by the strengthening yen that they have sent signals they might intervene to stop it. Earlier this month, Honda Motor Co.’s president warned that the pumped-up yen could cause the “hollowing out of Japanese industry.”

“Both countries are very dependent on exports, with very little domestic growth,” says Adam Posen, an economist at the Peterson Institute for International Economics. “Bad news is coming, and the dollar going down is additional bad news for them.”

Of course, there are upsides to a having a stronger currency in some corners of the globe. The dollar’s turn lower has brought a modicum of relief in emerging markets, where currencies have been battered in recent months. That is easing the burden on companies with debts to pay in foreign currencies.

For the U.S. in particular, a weaker currency could be a welcome help on another front — avoiding a cycle of declining prices.

“There is a pretty compelling argument both in theory and in history that if your problem is deflation, then pushing down the exchange rate is an effective way of addressing that problem,” says Barry Eichengreen, an economist at the University of California, Berkeley.

Mr. Eichengreen notes that, during the Great Depression, it was difficult to use a weaker currency to export more because of protectionist policies in place around the globe. However, it was a useful way to change people’s expectations about prices, since imports become more expensive. When the U.S. devalued the dollar in 1933, he said, the prices of some commodities, which had been spiraling lower, suddenly began to go up.

One fan of this line of thinking: Federal Reserve Chairman Ben Bernanke. In a 2002 speech, Mr. Bernanke noted that the devaluation of the dollar and the rapid increase in the money supply in 1933 and 1934 “ended the U.S. deflation remarkably quickly.” He described the episode as an illustration of what can be achieved “even when the nominal interest rate is at or near zero.”

That, of course, describes where the Fed’s key interest-rate target sits today. The fact that the Fed has been willing to embrace unconventional and aggressive lending measures carries an implicit message, says David Gilmore of Foreign Exchange Analytics, a Connecticut research firm, namely that “a weaker dollar in an orderly way is certainly a desired outcome.” He adds that the Treasury Department has avoided its usual mantra in recent months in which it reiterates its support for a strong dollar. The current problem, he says, is that “every country on the planet needs a weak currency right now, and not everybody can have one.”

In late November, China briefly pushed its currency, the yuan, sharply lower against the dollar, raising fears that it could be seeking a competitive leg-up. Since then, the yuan has recovered those losses. In Vietnam, where the local currency, the dong, is pegged to the dollar, the central bank devalued the currency on Wednesday for the second time this year. The move will help facilitate exports and control the trade deficit, the central bank said in a statement.

In the late 1990s, a number of emerging markets from Asia to Russia faced financial crises and were forced to devalue their currencies. Eventually, that helped spur economic recoveries by touching off export booms at a time of buoyant demand elsewhere. Today, though, the whole world is reeling, making it difficult for a country to export its way out of trouble.

“The world can’t depreciate [its currency] against Mars and export to the rest of the solar system,” says Simon Johnson, a former IMF chief economist.