Usually happens when the car is cold and I am starting off. It's a vibration from the passenger side. It usually goes away after the metal heats up, which means by the time I get it to the dealer 60 miles away, there's no noise. There is no clunk (described in other threads). Something is vibrating against something else. Pushing in the clutch makes no difference in the sound, except that I am no longer accelerating. I thought maybe the exhaust system. Or something is loose. The sound is always on acceleration and then it goes away.
I drive a 2002 MCS with 60,000 on the clock.