Most shows that are not Mickey Moused have a stock set of instrumental BackGround Music (BGM) to use as themes for particular characters or sequences, or simply to set a mood. These usually fill up the bulk of a show's soundtrack, aside from Theme Songs and (in the case of Anime) Image Songs.
The pieces that are most closely tied to characters or events are Leitmotifs.
For when it's not so much in the background, see Sorry I Left the BGM On.
For further exploration of this topic, listen to Anna Russell's "The Ring of the Nibelungs (An Analysis)".