If we’re talking audience participation, Sleep No More should definitely get a mention. It’s a theatre show where members of the audience are given a creepy plague doctor mask, instructed not to speak or take the mask off, and set loose in a warehouse-turned-hotel set. There you can wander at will, touching, reading, or even eating whatever you wish. While this happens, actors wander throughout the set, performing scenes from Macbeth. If you find a particular actor interesting, you can follow them, and sometimes they will involve you (grabbing your hand and leading you to another room, for example).
I’ve never been–it’s only been in London and New York, with, I presume, no plans to go elsewhere–but I’ve heard nothing but good things about it, and if it ever comes to Minneapolis, I am dropping everything and going, like, yesterday.
As for general theatre shows, others have given more eloquent reasons, but here’s my two cents anyway: I have seen certain plays more than once (and I’ve performed, as well, which means attending more than once just by default). It really is a different experience every time. It may be the same story, but the actors are able to play to different audiences. And when the show involves audience participation, all the better.
I went to a lot of plays as a kid, and the cool thing about theatre for children is that sometimes you get to meet the actors afterward. It always seemed so much more personal for me, to be able to see these people in person, speak to them, and know that, say, the cruel villain isn’t actually a cruel villain in real life. Meeting a film actor is a LOT harder to do. (Not that it’s easy to meet a Broadway actor, either, but you’re still seeing the actor in person, as opposed to a big screen hundreds of miles away.)