I finally made it over to Green St (in Cambridge) to try their much heralded burger, and I have to say I was not disappointed in the least. It's a great burger that will totally satisfy purists (such as myself), as they don't try anything crazy and hit all the notes just about right. The structure is two patties, about 1/2 inch thick each, topped with some mild cheese (I have to admit I'd had a few drinks and didn't pay close attention, but it was nothing weird or distracting). The patties were griddled very nicely, precisely medium with plenty of juice and fat. The beef flavor wasn't enormous, but certainly satisfactory and well-seasoned.
The burger also comes standard with bacon, which while misplaced off to the side, was perfectly crisp and thin enough that it didn't get in the way. The bun was standard, cheap, squishy and white--just how I like it--although a touch dried out. And the thousand island-y sauce was solid. The greenery was good quality and fresh. In fact, the only real downside was the homemade chips, which while fine were unsalted and cool to the touch. I would have preferred fries.
This definitely enters my pantheon of great burgers in the area, along with Flat Patties for a more fast-food style, and Highland Kitchen for more of a pub style (though not that thick). I'll have to try it again, but it could even be my favorite of the three. I'm surprised that J Kenji Alt didn't make it here (http://chowhound.chow.com/topics/614709) or chose to omit it, as I think serious burgers will agree that Green St's is very good. The only downside is the somewhat high price ($11). I'll try to assess whether the ingredients are high enough quality to justify the price in future encounters.
Thanks to those who recommended it! And the Buffalo Maine Shrimp were also pretty darn good.