What a great discussion! I agree with those who have suggested that playing music during free play can be counter-productive as it can cause some sensory overload in some children and be simply too loud for peer-to-peer interactions. Playing music during free play also prevents play in the music center. If you have a music area, then recorded music might be played to dance, sing along, or play along to, but it will be chosen by the children. Of course, this presupposes that the children have access to some recordings and something to play them on and can operate the device independently.
Several posters already identified wonderful opportunities for incorporating music: transitions from one activity to another, practicing executive functioning skills (impulse control, sharing, etc), signaling requested actions such as cleaning up, enhancing circle time, or as an intentional stimulus for process art.
For some children, the addition of music in learning social-emotional or academic skills can open up a whole new arena of learning and processing. Music's inherent power comes from the ability of melody and harmony to attract attention and beat and rhythm to organize the auditory input into something the brain can process.
I really hope this conversation continues!