Is it doing it ONLY while driving, or does it do it at idle in park or neutral?
If it only occurs while driving, I would suspect it is something in the driveline like U-joints or something along those lines.
If it does it in neutral or park, while the car is not moving, I would suggest inspecting the harmonic balancer. Watch it while the car idles and look for any wobbling or wiggling. Sometimes it is easiest to notice it by actually watching the belt and seeing if it appears to track back and forth as the crank spins around. Also, a tell-tale sign of a bad harmonic balancer is that the rubber on the back side of it (toward the firewall) will begin to bulge out. Sometimes it will be bad enough that you can actually see it pushing out of the harmonic balancer. Finally, you could also check the timing. Assuming you know where the base timing was set (or at least have an idea - it should be somewhere around 10 BTDC), you can pull the SPOUT connector and hit it with a timing gun. A really weird base timing (for example, 25 ATDC) would indicate that the balancer has likely spun, as the chance of the car running when the timing is that far out is pretty small.
2006 GT - Vortech polished w/ intercooler, Eibach suspension, Hurst short-throw, some other goodies - tuned by Paul's High Performance. It moves...
and it collects dust admirably while parked for repairs in the garage...
SOLD - 1995 Black Mustang GT, AODE. Loved it, but I had to let it go...