If it happens when you are driving fast (60-70 MPH) it could be that your wheels are out of alignment.
i would really like to know myself
Brake rotors are warped.
You may have a bent wheel, defective tire where a steel belt has shifted or broken, worn steering parts, and possibly a defective wheel bearing.
Your power steering pump and or steering box may be about to give out on you.
A shake in the steering wheel or car itself which occurs and/or increases as vehicle speed increases.
If your steering wheel is shaking you probabley messed you wheels or axel up
have front suspension checked
If other things vibrate as well as the steering wheel you might have a damaged motor/transmission mount.
Steering wheel was installed upside down or the steering wheel is turned 180 degrees.
Get the tyres checked for balance, and bulges in the side wall.
Right side of the road, left side of the car for the steering wheel.
You probably need to get your tires balanced. Or replaced. If the bias goes (steel belt breaks or shifts), the car will waddle at low speeds, and the steering wheel will shake at high speeds.