Real New Yorkers don't go to TKTS, the Times Square booth that sells discounted same-day theater tickets. (Or if they do, they don't tell anyone and deny it vehemently if asked.) But that doesn't mean that we locals pay full-price — at least not if we can help it. TheaterMania.com offers excellent reductions (typically 35—50% off) on Broadway, Off Broadway and Off-Off Broadway tickets. Right now they have 19 Broadway shows on offer, including two I can personally recommend (Avenue Q and In the Heights) and two I really want to see (Speed-the-Plow and 39 Steps).
There's no catch: you just sign up (for free) and then they give you a discount code to use when you purchase the tickets online, on the phone or in person at the box office (which lets you avoid the service charge). The ticket prices vary according to seat location and weekday vs. weekend — an orchestra seat on Saturday night is a lot more than one on the rear mezzanine on a weeknight. But all of those differences are clearly spelled out, and yes, you do get to choose your seats as usual.
So, if you're able to do a little planning, Theatermania is the way to go. It's very cold here in New York right now and you don't want to get stuck waiting on the TKTS line. Not when there are so many better ways to be spending your time in the city.