These are the tires that I use:

http://www.schwalbetires.com/bike_ti...res/ultremo_dd

It's not cheap, and it will wear fast (1,500 - 2,000 miles useful life depending on weight of bike/rider), but it is very sure footed and grips well in the rain or dry. That said, I don't commute in NYC so I have no comprehension as to the debris that you guys encounter. The Ultremo DD is still a very light racing tire and something viscious will still puncture the tire.

The ultimate in puncture protection for a road bike (at least from our stable of tires) is the Durano Plus. Still a nice gripping tire, probably the best puncture protection on the market for this kind of tire, and very long lasting. The downside is, they are a bit heavier (about 100 grams more than the DD). http://www.schwalbetires.com/bike_ti...es/durano_plus

I know we aren't the only brand out there, but those are the 2 tires that I'd recommend based on your stated requirements.