One of the most popular ways to save big on Broadway and Off-Broadway shows is to stand on line at one of TKTS' three discount booths, located in Times Square, South Street Seaport, and Downtown Brooklyn. Check each individual booth's hours on the site, and note that times for purchasing matinee and evening tickets will differ. At the Times Square TKTS location, on Broadway and 47th Street, which sells only same day theater tickets (matinee and evening shows), you'll be closest to the shows you're most likely to see, but you'll also probably wait on a much longer line, up to an hour or longer on weekends. Why not plan ahead and travel instead to the South Street Seaport booth, at Front and John Streets, or the Downtown Brooklyn booth at Metrotech Center on Jay Street? At these locations, you can buy tickets to evening performance for the day-of the show, and matinee performances one day prior to shows, and you'll rarely ever have to wait more than five or ten minutes in line, if there's a line at all. Discounts at any of TKTS booth range from 25%-50%. The only drawback is that your chosen show may not be offered at a discounted price for the day you wish to see it. You need to come to these booths with an open mind, check this site for the prior week's sales to see if your show is on there, and be prepared to have a backup option or two.
If you do have one particular show in mind, try these websites for deep discounts:
Broadway Box, Theater Mania and NY Tix all provide discount codes for FREE, that will earn you up to 50% off of face value of theater tickets, and can often be used for either online, ticketmaster, telephone, or box office purchases. NY Tix has a particularly helpful list of currently available discounts and lineup times for "rush" tickets (see note about rush tickets below).
Playbill Club: You must sign up on their website and join the "club" in order to access discounts, but membership is free. Discounts on theater tickets range from 10% to 50%.
Score Big: This is a very new website and members currently can only join (for free) by invite, or by getting on the waiting list. If you can get on the site, it is well worth it. Score Big is for theater and other event tickets what priceline is for airfare/hotels/travel. You are "guaranteed" to get a deal by bidding on tickets for lower than face value, and seeing whether or not your bid is accepted.
Hip Tix: If you're between the ages of 18 and 35, sign up to receive $20 ticket offers to broadway and off-broadway theater, sponsored by Roundabout Theatre Company (but be careful, once you're on Roundabout's calling list, they'll never leave you alone...).
TDF: TDF, the Theater Development Fund, not only runs the TKTS booths, it also offers an online ticket program for "eligible theatergoers," which includes teachers, retirees, civil servants, non-profit workers, union members, students, armed forces and clergy. It requires a $30 yearly fee but if you go to even 1-2 shows, your discounts will pay off.
Plum Benefits: If your company doesn't already have a Plum Benefits account, talk to your HR manager today! You can only access PB if your company signs up. I have ordered so many great tickets from this site and saved a lot of money. PB offers discounts for theater, sporting events, concerts, comedy and restaurants.
Many productions also offer "rush" or at least student rush tickets (purchased via waiting on a line a few hours before curtain and being subjected to a lottery system, but you usually get great seats), and standing room only tickets. Call the box office for more details.
Another idea is to go to your local library, college or community center and see if you can get "school ticket" discounts. These are flyers, about the size of bookmarks, that advertise the show and also provide discount codes for a finite time-period. Although they are known to be "school" discount tickets, and are most often found in some principal's office, you don't actually have to be a student or school administrator to use the code. You just have to know where to find one...