If you hear a metallic scraping sound when you brake in addition to shaking you could need new disks (brakes) because they are warped. If it only shakes while moving and you don't hear anything funny your tires could be miss aligned/un balanced -uneven tire wear can cause shaking feeling.
Is it an automatic? Does it shake when the automatic transmission shifts? You may need to replace your transmission fluid. Your transmission may have some other problem, as well.
If it only shakes when you press your brakes, then get your brakes replaced NOW!!! You have likely burned out your pads and are actually stopping your car with your calipers, rather than your actual brake pads.
If it only shakes when you press your brakes, then get your brakes replaced NOW!!! You have likely burned out your pads and are actually stopping your car with your calipers, rather than your actual brake pads.