It's getting much more common among places that care about getting good developers. I've implemented this practice myself where I'm involved in hiring, although when it occurs in the process has varied. It's always been after the initial phone screen, but before/after on-site has varied. I tend to prefer it after, e.g., phone screen, short on-site to suss out major compatibility issues, take-home drill(s), then longer on-site if the code passes muster.

You can find out a lot about how a person thinks about programming with exercises that take actual time. Twenty minutes with FizzBuzz (which I still get on occasion) doesn't speak towards anything beyond "can monkey type?"

I've made it a rule to provide fairly detailed feedback if I get to the point of giving someone an exercise. Not all places do that, and I think it's too bad. If someone goes to the trouble of spending their free time on this I feel I owe them at least some of mine.