The dollar has always been a safe-haven asset in recessions, but not with respect to the euro this time
In past recessions, the dollar has always appreciated significantly against the euro, and against all currencies. The dollar (and the Treasury market) played a safe haven role. Today we can see that this is the case against emerging countries' currencies, but not against the euro, despite the capital flows from emerging countries that are boosting the dollar. The reasons why the dollar is not appreciating against the euro today is probably that: The ECB's and Europe's reactions this time around will prevent the risk of a break-up of the euro zone; The drastic rise in unemployment in the United States, leading to an increase in defaults on mortgage loans, may make the crisis even more severe in the United States than in the euro zone.