as comatosellama suggested, speed dependent vibrations/shaking are most often caused by a tire out of balance, sometimes a damaged tire - Start there.
As texan suggested, swapping tires from front to back for a quick, inexpensive test.. if the vibration is still present, bet less noticeable in the steering, that would suggest it IS a tire out of balance and/or damaged. get them checked
If swapping the tires has no effect on the vibration/shaking, then yes, you need to dig deeper.
potential issues: ball joints, tie rod ends, wheel bearing, CV joint (axle), maybe a frozen brake caliper.. also check struts & springs..
also take a look at the lower control arm mounting points. the rear most mount bushing tends to be a problem area