For some shows in the
Theatre District, theatres sell
tickets for the day of performance for their respective shows at very low prices. To get such tickets, you might have to go to the theatre's
box office early in the morning (depending on the popularity of the show and traffic of the ticket buyers).
I have seen a handful of shows in Broadway by buying rush tickets. I have seen Chicago: The Musical, Cabaret, and Putting it Together by buying tickets when I wanted to see the shows as opposed to making advanced reservations.
For some of these shows, a few seats at a specific section in said theatre will be reserved for an occasion. Cabaret has the rear mezzanine row available for Monday-Thursday performances, Chicago: The Musical has the front row to the back of the orchestra (standing room), and Putting it Together has seats available from the rear mezzanine (if you ask the box office folks in the Ethel Barrymore Theatre) to anything else that is available (if you have the "student tickets" coupon in one half-hour before the show).