If you've ever seen an American movie from around the 1940s and earlier (and if you're reading this in the US you probably have), you might have wondered why the performers sound so different from actors today. This video from HowStuffWorks explains the accent, referred to as the Mid-Atlantic or Transatlantic accent:

It's not just actors from the time period, but also anyone from higher class society at the time:

This type of pronunciation is called the Transatlantic, or Mid-Atlantic, accent. And it isn’t like most other accents – instead of naturally evolving, the Transatlantic accent was acquired. This means that people in the United States were taught to speak in this voice. Historically Transatlantic speech was the hallmark of aristocratic America and theatre. In upper-class boarding schools across New England, students learned the Transatlantic accent as an international norm for communication, similar to the way posh British society used Received Pronunciation – essentially, the way the Queen and aristocrats are taught to speak.

If you're from New England, you've probably heard the accent from older speakers who grew up around this time. As for performers from this era, since this was the prevailing accent of upper-class societies, it was also the one most commonly taught to actors. Though it fell out of use around the same time people stopped using it in common society, you can hear it in plenty of older films. Method acting and other more natural styles distanced themselves even further from this put-on accent, and strived for more authenticity in the performance, which meant accents that sounded more like real people, and more appropriate for their characters. 

For another example of the Mid-Atlantic accent, here's Katharine Hepburn and Cary Grant from The Philadelphia Story:

And for fun, here's Australian Cate Blanchette doing the accent as she plays Hepburn in The Aviator:

For a bit of contrast, Emma Stone talks about how she prepared for Gangster Squad with a Mid-Atlantic accent (since it takes in the 40s), but director Ruben Fleischer wanted something a bit more natural-sounding:

At this point it's an accent we tend to make fun of (usually in a good-natured way), but as realism entered American cinema, the writing would have already been on the wall for this kind of fake, non-descript Mid-Atlantic accent even if it hadn't started falling out of use earlier than that.

Source: HowStuffWorks