"The crosswalk button is a relic of the age before computer-controlled traffic signals. In New York City for instance, “the city deactivated most of the pedestrian buttons long ago."
Then there is the close door button on elevators. "According to a 2008 article in the New Yorker, the close door buttons included in most elevators since the 1990's do not actually work the way passengers think. The buttons are installed for emergency personnel, not for the general public. Firefighters use the buttons to open and close doors between flights, but they can do so only with a key or other special instructions."
Office thermostats are another example. "If you work in an office building, there is a good chance your attempts to regulate the temperature in your office are just as futile as pushing a crosswalk button. With the advent of building-wide control systems, individual office thermostats often do little more than decorate the walls."
Read the article in the link for more details on the buttons.
And next time you encounter them, realize that you are probably not actually doing anything.