Video keeps starting and stopping

The videos on this site have been designed to playback at a data rate of about 416kB/s. This means that in order to play without stopping you must have a minimum download speed of 512kB/s.
If you have an internet connection that is at least this fast and you are still having trouble, look for other applications that might be using your bandwidth, and disable them (Windows might suddenly decide that it needs to protect you by downloading a huge update).
One foolproof (but tedious) way of fixing this problem is to hit the pause button on the player and wait for the entire movie to download (as indicated by the shaded bar under the slider).