Could be the catalytic converter.  They often go bad and break up
internally so they rattle badly when it happens.

what kind of noise?

Drifter
"I've been here, I've been there..."

ganggreen82 proclaimed:

  What drive train?  What kind of noise.

  If a passenger in the front seat hears something from more or less
  under the vehicle, check the exhaust system for being loose, your
  cat convertor for rattling.  If it comes from further back, check
  the rubber rear exhaust mount for being too old and letting the
  pipe whack on the rear suspension on bumps.

I'd check the exhaust system like everyone else has suggested, but I'd take
a look at the shock on that side as well. You may have a broken mount.

Nat Man