First to be younger than me (October 10, 2002): Ales Hemsky (1983/08/13), Jay Bouwmeester (1983/09/27), and Rick Nash (1984/06/16)
My guess is that either Bouwmeester or Nash played first as they played in the Eastern time zone that day, but NHL.com doesn't have game times that far back.
NHL Players still older than me: Matt Cullen, Zdeno Chara, Joe Thornton, Patrick Marleau, Chris Kunitz, Brooks Orpik, Niklas Kronwall, Ron Hainsey, Derek MacKenzie, Matt Hendricks, Justin Williams, Deryk Engelland, Andy Greene, Tomas Plekanec, Jason Pominville, Dan Hamhuis, Mikko Koivu, Ilya Kovalchuk, Chris Thorburn, Jason Spezza, Roberto Luongo, Ryan Miller, Craig Anderson, Henrik Lundqivst, Mike Smith, Peter Budaj, Pekka Rinne, Curtis McElhinney