The first thing that comes to mind if the "clunk" is only on starting is worn or broken motor mounts. Something is moving and allowing things to hit each other. A clunking that is intermittent while running may be a ball or roller bearinng going bad.
You're a clunk-head...
could be bad mounts on either the tranny or engine?
Sway bar bushings
Check for Rheumatoid arthritis. Cervical spine X- ray.
Just out of curiousity, how is the transmission in this vehicle. Could the transmission be out of sync with the engine? This has happened to me when i had the transmission replaced in a dodge caravan, Good Luck
You have either run something over or your car is due for a service
The rubber isolators in the engine mounts have worn out or the CV joints in the drive shafts are worn out.
It could be many things. Go get your car checked.
The Transmission needs SERVICED A.S.A.P Hope This Helps.
Year, make, model, engine size, etc. does help. Possible engine mount, u-joint differential,trany, etc...
Worn CVC joint. Could be bad struts causing the spring to bind. Depends how severe the clunk is. If it is struts, it sounds like the floorboard is getting hit by a sledge hammer.
check engine mounts