Chumly's still exists. For a while, the neighbors stopped them from using the courtyard entrance, so you'd have to use the street entrance, but the last time I went by there, it was open again. It's at Bedford & Barrow, between Seventh and Hudson.
My favorite (although I like the Subway Inn too) used to be Puffy's Tavern in Tribeca. But about a year ago the owner sold the place, and the new owners got it into their heads to rennovate. No one bothered to explain to them that a cleaned up dive bar is an oxymoron.
Years ago I liked Canon's up on 108th Street and Broadway. But they closed about a year ago -- the family, which also owns the building, decided they could make more money renting the space out.
Does anyone remember that dive bar that used to be across from the New York Times building on 43rd Street? It was called Goughs (pronounced "gofs") and a lot of NY Times staffers were regulars, although mostly it was the pressmen (when they used to print the paper there). It was one of those places that hadn't changed since the early part of the 20th Century, with old sports posters from the teens and 20s still up on the walls (never been moved since they were originally placed there). That place was torn down in the 1980s.
Another rennovated dive bar that used to have a lot of character was Yankee Tavern a block from Yankee Stadium on Grand Concourse. They also served a really fatty corned beef sandwich there. You needed several beers to keep it down!