I personally feel that we have seen a huge shift in the way the public interact with world around them because of the more interactive internet which has evolved over the past decade.
Just as people no longer just see the internet as a place to find information, I think that the public no longer expect didactic experiences from museums, they instead want cultural institutions to be platforms for exchange, places that accept that anyone can have a valid point of view.
One element is having a say what goes into museums, this could be by submitting work through an open call for entry, voting from a shortlist for what should appear in an exhibition or interacting with an exhibition in the gallery.
Though I believe strongly in the public being given a voice, personally I feel that the majority of an exhibition programme should still be curated in a traditional manner.
Museums have a many other ways to give their audiences a voice, one of those which I find particularly interesting is simply asking those in the gallery space how they feel about the art on display, and sharing this with others.
I have seen museums do this through comment cards pegged in the gallery, writing with chalk on the wall around the paintings, through text messages, video and through the web. By sharing their opinions on art with other visitors, you see a dialogue emerge, this creates a different starting point from which others can approach and appreciate an exhibition.
Often these starting points are not the same as those you would find in a curatorial description of a work of art, but they are just as valid and often make you look at art in new and unusual ways.