Axcents.

As you may know, I grew up within the friendly confines of the Five Boroughs, raised by parents who had grown up in Brooklyn and Queens. My father was a real dese-and-dose guy, possessor of a classic accent most associated with New York. A friend of mine had fun with the meme generator regarding the way we speak:

The last one's an expression rather than an accent, but ask anyone who grew up before 2000 in the city what they call ground beef and you're likely to be told chop meat.

The New York accent has spread to New Jersey, counties of the lower Hudson Valley, and a good ways out into Long Island, as the blue-collar population moved to the 'burbs in fits and starts in the postwar era. But what we think of as the New York City accent is much different from what people in the Civil War period considered a New York accent. I don't know much about it, but some examples of now-extinct northern American speech are detailed here.  

What people consider a street-level New York accent was spread and has been perpetuated by the movies. Wise-crackin' cabbies, surly cops, gum-chewin' secretaries, tough private eyes, all kinds of New York City working stiffs populated the pictures, and America loved 'em. 

Curious accentologists will find a good summary at a Wikipedia page, believe it or not. It notes that some of the classic features formerly associated with the New York accent, like goil for girl, are extinct in practice. I suspect that the spread of Italian Brooklyn accents in New York wiped that out, making the New Yorker sound less like Moe and Curly ("a woise guy, eh?") and more like Vinnie Barbarino ("Whussup?"). 

Obviously the city has been crisscrossed with different ethnicities and languages and foreign accents over the centuries, making an ever-changing mélange. I wouldn't want to be a professor of this stuff, because by the time you catalog it, it's different. O. Henry wrote of New York, "It'll be a great place if they ever finish it," but that will never happen any more than the accent will stay put.