Whistle while you work. Whistling a tune is a very easy way to make music with your mouth. It's rather creative as well. You don't see enough pop hits that include a good whistling track.
Watch "The Little Mermaid." Ariel sings a very familiar tune with no music when the witch takes her voice away. It is repeated in the movie. Watch for this, and try to imitate it. Keep the "ah" sound open with your mouth.
Try humming your favorite tune. You can even make this a game by challenging your friends to name which TV theme song you are humming. Hum on a track if you are laying down a record. Humming is definitely something that our mouths can do to create fantastic music that is instantly recognizable.
Try clicking. You can click to the beats with your tongue. it makes a very similar noise to snapping your fingers. Try doing it over a hip hop beat. You'll definitely get in the groove with that slick move.
Harmonize with a friend. Use your voice to sing the same notes in unison. You can create a beautiful harmony with nothing but your voices!