First thing to check is shocks/struts. If they're sloppy, they're just letting the front wheels bounce around uncontrolled. (couple that with lumpy tires and you're in for a rough ride!)

Could also be tie rod ends, but you'd feel that as play in the steering wheel, as well.

Ball joints are also a possibility, and to a lesser degree, wheel bearings.

To check all but the struts, jack the car up, grab the wheel and push-pull it left and right and up and down. Feel for any movement. If you don't feel any clunky movements in any direction, then your tie rod ends, ball joints and wheel bearings are probably okay.