Most of them do not work, this 8 year old NYT article claims that 120 out of 3250 signals in NY work a decrease from their census in 2004 and mentions how a different agency found 1 working button across various cities. The only ones that kind of work in my experience are in New Jersey, where if you do not press the button, the intersection will never clear you to walk. The signals and everything work the same, just you will never get walk at the intersection (even when you normally would have) without pressing the button.