What is wrong, if anything?
 

Sometimes when I am driving my 986 2.7, there is a sudden loud vibration coming from behind me. I thought that the wind deflector was just shaking more than usual, but when I held the wind deflector down in place, the noise was still there, so that was not it.

When I step on the clutch or put it in neutral, it stops. This rarely happens. Does anyone know what it could be?

FYI: I have the check engine light on for the secondary air system like most Boxsters get sometime in their life. I plan to replace the cut-off valve when I make the money. But I doubt that has anything to do with the vibration. No other CIL codes or warning lights. Wheels are on tight. Tires are in great shape.

engine mount?

Is the vibration around 3000 rpm? If so, join the club. As was suggested, you could try replacing the motor mount (as I intend to do this spring). Others say its the clutch. Others say its the exhaust. A forum search will get you lots of hits.

Engine mount is exactly what i was thinking. It was around 3000rpm.
Exhaust feels tight to me. I don't see how the clutch can make that kind of noise. It's got to be the engine mount.