As an aside, with the recent Supreme Court ruling on gay marriage and everyone pointing out how the United States is behind relative to Europe, I would like to point out that gay marriage United Kingdom (unless I am misunderstanding/misinterpreting wikipedia) only fully legalized gay marriage starting March 13th 2014, and that Germany has not fully legalized Gay Marriage (only Civil Unions) as of now so, I wouldn't say America is to far behind on that issue.
However, that being said, it does seem America has generally been behind ( I know this is sort of a subjective term, but bare with me please) on social/political issues relative to Europe, and even other parts of the world sometimes with issues such as healthcare for example. In fact there are a few issues the United States is extremely behind on, such as paid maternity leave.
So was there any time America was collectively very progressive on a certain issue relative to Europe or the world in general?
The Public Health Cigarette Smoking Act of 1970, banned Cigarette commercials from television and radio, in 1971. Restrictions on smoking on airplanes, in bars and other public places became more comprehensive between 1971 and 2004. Cigarette advertisements were banned in print media in 2004. NASCAR even had to change the name of their championship trophy from the Winston Cup to the Nextel Cup. In Europe, tobacco companies could still sponsor Formula One teams as late as 2006.
The US moved very quickly to extend the franchise, though many of course remained excluded. And it was a pioneer in separating church and state. And "All men are created equal" beat France's National Assembly by thirteen years, though of course it didn't apply to all men, or women. The 19th-century education record is mixed but positive compared to much of Europe, with early public schooling but incomplete enrolment, and high literacy but many again excluded.
I suppose (this just occurred to me) that America set a great precedent on the idea of National Parks, but other than that any other answers would be appreciated.