Yes. We do it from time to time. Obviously, it's not anything like the movies. We only use grips and grabs, not strikes (as attacks). It really helps students (over time) develop both the ability to identify an attacker's body position based on the attack, and their ability to "sense" an attack coming by the sounds of how someone moves. That latter requires a very quiet training space, and students learn to pick up a lot of information from scuffing of feet and rustling of clothes. It doesn't translate into being able to fight in the dark against people with night vision on - no ninja stuff here. It does translate to a better sensitivity around attacks, allowing better responses without having to look, and sometimes without having to turn their head. Think of it like the no-look passes you see sometimes among professional basketball players.
Unfortunately, I did get hit quite a bit. 
Yes, not often, but we do use it. Since Wing Chun involves tactile feel, blindfolded training helps to test and experience this feel at a heightened level than when using your eyes.
It was a testing requirement for belts when I took jiu jitsu. what effect did it have? Most people compensated with power. We would do a blindfold circle with the person being tested in the middle, and the ukes surrounding them grabbing them in semi random fashion. As our style emphasised blow throw blow, if you couldn't see, you had a tendency to strike harder. Occasionally you would see some finesse.
Frank,is that you?
