This is most likely caused by your car being out of line. You can get your tired realigned at most auto shops. This will eventually wear on your car, mostly causing you to have to get tires sooner than what you should have to. If it does it when you use your breaks, your rotors could be warped.
Vibration can be dangerous to the point it shakes the wheel out of your hands. Have a shop check you suspension to make sure all the components are in good shape and everything is tight. Also make sure your wheels are all correctly balanced and that they are properly aligned.
Either the car is severely out of alignment, or it could be as simple as having just one bad tire. One bad tire that is usually about to break or burst will cause the whole car to be off balance causing it to vibrate severely at higher speeds.
At high speeds, the alignment of the vehicle becomes much more noticeable. You may notice that your car has a tendency to go in a direction that is not straight if left on its own. The wheel vibrates from there being a lack of efficient installation amongst the tires and the axels.
High speed wheel vibration can be caused by a number of things. A tire being out of balance, bent wheel or rim, tire that is cupped or flat spotted, bent axle or even a bent tie rod can be causing the vibration.