This is a good question and a tough one, obviously...since I haven't listed just one.
Play - although the Pillowman is the play that impacted me the most, I would probably recommend Doubt. Both were sensational, but many people I know would not appreciate the distrubing aspects of Pillowman. Doubt I could recommend without reservation.
Musical - surprisingly for me, I would recommend Dirty Rotten Scoundrels for people who want a night of fluff and lots of laughter. I had spent months waiting for Spamalot. I enjoyed it, but not as much as DRS. I think everyone should witness Norbert Butz in this show.
For a evening of pure theatrical and musical beauty, I would recommend Light in the Piazza.