Regarding the classic Straight Dope column that was rerun on the website today:
http://www.straightdope.com/classics/a3_153.html
I have an story of an example when a “Push to Walk” button did actually work, although I don’t know if this really counts for anything because I think the signal may have been broken to begin with.
My fiance and I were in his car, and had driven down the end of his street, where there is an intersection with one of the major streets in town. We were planning to turn left, there was another car ahead of us, and the signal was red.
We waited a minute, then another minute, then another. Cars pulled up behind us and the line of cars waiting at the signal started getting really long. When it had been about 4 or 5 minutes, my fiance wanted to try and turn around, but there wasn’t much space to do so, with all the other cars around.
So I had an idea. I got out of the passenger side, ran up to the corner and pressed the “push to walk” button. By the time I got back inside the car, the light had just turned green and we were able to move. This probably doesn’t prove anything, since as I said, the signal seems like it was broken to begin with (the red light has never been that long, either before or since) but I just happened to think of this story when I read the article.