What is making my car shake while driving?

Multiple possibilities. Warped rotor or poss. broken belt in tire, tire balancing problem, alignment issues. Also, bad tie rod or ball joints in suspension. Best to have a suspension shop check and diagnose. Even busted motor mounts.

Agree with cb30, also is the check engine light on? Engine skipping, misfiring?

Sounds like you might have oneb or more cylinders missing.check spark plugs, wires distributor cap, rotor button.