There is still, five (or whatever) years after the most recent change in fiction editor, a recognisable type of New Yorker short story. Of course, any magazine that publishes new fiction on a weekly basis is to be cherished, but for the most part you have some idea at least of what you are going to be getting. Occasionally, though, something comes along that surprises and stays in the mind. That goes back to the 1940s, actually, with the publication of "The Lottery", by Shirley Jackson. (Salinger's Glass family stories, come to think of it, don't really look like anything else, either.) The surprises in my own reading lifetime include a remarkable horror story by Nicholson Baker about (not a typo) Mister Potato Head; the first piece I ever read by Roberto Bolano (whose "The Savage Detectives" I have just finished reading, after toughing it out for almost a year; it was the opposite of a page turner until the last fifty pages or so; but I finished it with the sense that I had just read something extraordinary, and also that I had completely missed what was actually going on for most of the book - I don't know if that is a recommendation or not, read it at your own risk!); "Super Goat Man", by Jonathan Lethem; and a story about a clown set in South America somewhere, name and author forgotten, sorry.
The most recent story to break the mould is "Baptizing the Gun", by Uwem Akpan, from the issue of 4 January 2010 - that's "twenty-ten". You can read it here. It tells the story of a night in hell as experienced by a country priest who is driving his brother's clapped-out VW Beetle when it breaks down somewhere in the badlands of Lagos, a city that, based on what I have read about it, might be a fascinating social experiment if there weren't millions of actual human lives involuntarily caught up in it. The story is a bit like "Slumdog Millionaire" but stripped of the bright colours, stunning cinematography and, y'know, "hope". Nevertheless I can, and do, recommend that you read it.