I watched it live (not on TV) in the sky from the playground of Ocean Breeze Elementary, about 20 miles south of the Cape. It was my 12th birthday.
It took a few minutes for it to sink in that it had exploded. We knew something was wrong, but the teachers wouldn't confirm that it had exploded - I think they didn't want to deal with a bunch of crying kids. We observed a lot of debris falling from the explosion. Some of the kids in my class speculated which of the pieces was the escape pod. We presumed that there had to be one.
Then we went inside and turned on the TV, where they just showed it blowing up over and over. We were all kind of numb. A couple of kids were worried about their parents losing their jobs. I remember kids at lunch making the joke, "what does NASA stand for? - need another seven astronauts!".