Do you actually mean "downloaded"? This is where you download the entire video, and then play it. If you mean "streamed", which is where (like YouTube) you watch the video as it downloads, the pauses will be caused by buffering, which is what happens when your Internet connection can't download fast enough to keep up with the player.
In the case of YouTube you can solve this problem by clicking on play, and then immediately clicking pause. The video will continue downloading (as indicated by the progress bar turning a lighter shade of grey). Once a reasonable amount of video has downloaded, click play, and as long as the red progress bar never catches up with the light grey section, the video will play fine.
If the red bar catches up with the light grey section, that means you are back to attempting to watch in real time, and the player will resume pausing to allow buffering.