Users occasionally hit their daily flag/vote/review/reputation limits which reset at 00:00 UTC, especially on Stack Overflow. There should be a countdown to 00:00 UTC so that everyone can see when will the limits reset.
I am not sure how and where you would see this. I don't see a place where a countdown would be a useful addition to the site. The main content is timeless, it doesn't have the need to show the time. The only 'useful' place is the review queue if you have run out of flags or votes.
The achievements dialog already has the UTC time. You could also just remember your offset to UTC once and calculate it back to your local time. Or you could add a second clock to your computer to show the UTC time.