Note: Be sure to read the comments for more help!
Today when I used the Snipping Tool in Windows 10 it stopped working. I could select an area over and over again, but it never closed after that as it should. The screen was dimmed and I could not get to any other program because Snipping Tool was on top of everything, even Task Manager! I almost gave up doing a hard reset, when I found a way to get rid of it:
Alt+Tab still worked though. There is a small X that appears if you hover an application thumbnail with the mouse. Using this you can close Snipping Tool!