Musical silence can be one of the most powerful “scoring” devices you can use.
It works especially well in scenes where you want the viewer to be pulled into the reality of that scene, especially if it is a very intense scene. Leaving out music in moments where usually there would be music eliminates that certain “cinematic distance” to the scene. Such moments work best when you have very strong and intense pictures.
Think of the opening sequence of “Saving Private Ryan”, which has an extremely intense character. Apart from the fact that music would feel inappropriate in that scene, the complete absence of a “musical comment” pulls the audience much stronger into the scene than it would if there was music. Of course, also the visual perspective from actually being involved in that scene with many shots from the first person view adds alot to this viewing experience.
Silence works extremely effective if it noticeable. Having a silent moment in an otherwise very actively scored sequence will highlight this moment even more. This is often used on climaxes of scenes but also punchlines of funny moments.
The bottom line is to be aware to not glue everything over with music but view “having silence” as another way to “score” a sequence/scene/moment.