Ok, so I know this is an old debate, but it's worth rehashing bc there's a new contender.
First of all, I have to say that the Dumpling Man is totally overrated. I don't know how that place got such good press, bc the dumplings are average at best. I am also not a fan of Rickshaw's dumplings which taste weird and 'americanized' if you will. Plump dumpling's product is much better than Dumpling Man's, notwithstanding the logo war between the two. Obvious other contenders are the Dumpling House and Joe Shanghai's famous soup dumplings. But add to the list Vanessa's Dumplings on 14th between 2nd and 3rd. Brand new and reminicent of the Dumpling House's stuff--they even use those huge metal vats to make them. I vote Dumpling House and Vanessa's #1, Joe Shanghai's #2, Plump Dumpling #3 and Dumpling Man and Ricksaw a distant fouth (regular chinese resaurants have better dumplings than our #4 contenders).