This Sinn aviator watch displays the most common approach - put a luminous (glow-in-the-dark) material on the hands and display markers. If they are "charged" with ambient light before you go in a dark place, you can see them glow. This particular watch is exceptionally efficient and is readable all night long.
Another way to do the same thing is to have a light-colored dial that glows in the dark. This Sinn watch uses a luminous material on the entire dial. It's not very long-lasting illumination, but you can read it for about 2 hours after you've gone to bed.
The Timex Indiglo watch uses a battery and special dial that glows when a button is pressed.
Finally, some watches, such as The Ball watches, or this pile of Prometheus watches, use tubes of glowing material. They do not need a battery or a sunlight charge in order to work, but make a nice display on your dresser at night!
Another way to tell the time, and a much older way, is to listen for bells ringing. On your wrist, we call this a minute repeater, or chiming watch. This is an extremely nice watch (a friend of mine has one of these). You press a sliding button on the side of the case to check the time, and it rings the hours, the quarters (15 minutes) and the minutes. The watch in the movie is going to strike 9 hours, 3 quarters and 13 minutes.
Clocks commonly strike the quarters and the hours - although modern ones have a blocking feature so the chiming doesn't wake you in the middle of the night. I have at least a dozen striking clocks - here is one that we have in our living room, about to strike 12.