I think a lot of games do neglect the power of music to a certain extent. But only those of certain genres. Some games have thoroughly grasp the concept of using music, and do so very well.
The final fantasy series would be a good example. Those use music very well. I know a lot of people, including myself, who were close to, or in tears when aeris died in FFVII. Try playing it muted, it doesn''t have nearly the same power. Similarly, the fight music is always very empowering music, and it absolutely works to get you in fight mode.
Another title that made a sucess of its sound design would be Silent Hill 2. Some of the music in it really put me on edge, and sent chills down my spine. Infact, there is a thoroughly amazing trailer for SH2 that I''ve got. It''s the scene with "Mary/Maria" behind bars, with the Guitar riff title music over the top. That trailer truely sent chills down my spine, and set the tone for the entire game imo.
I''d rip it off the cd and upload but I don''t have a DVD drive

I''d certainly agree though that certain genre''s have neglected music as a powerful tool to invoke emotion for a long time. From what I''ve seen, that''s starting to change.