That vibration you are feeling and that clunking you are hearing as you accelerate and decelerate is likely coming from your drive shaft. When this part starts to fail, you'll know it. It can lead to all sorts of problems, both big and small. On the small end, a failing drive shaft can send intense vibrations through to other parts like your rear differential or axles, causing harmonic disturbances and premature wear. In a larger sense, the yokes holding the universal joints could completely snap off and you could lose total control over your vehicle. Either way, those are expensive problems to repair. If you know that these could be the potential results of driving with a bad drive shaft, then get it fixed pronto. There's no reason to let it go on any longer if it can be helped.
If you have a rear-wheel or all-wheel drive car or truck, then you have a propellor drive shaft running from the transmission or the transfer case all the way back to a rear differential. Its job is to deliver the torque from your transmission to the rear wheels. It is usually interrupted by one or more universal joints. These joints allow for the parts of your drive shaft to keep rotating at the same velocity while the ends change elevation. Since your car or truck may go over bumps or through pot holes, the front and rear suspensions, axles, and wheels aren't always at the same height. The U-joint makes sure your drivetrain allows for these changes without affecting its speed. Your drive shafts must also be balanced by the factory, which means that the weight around their edges must be evenly distributed. Otherwise, it will wobble and create very unpleasant vibrations.
Replacing a drive shaft can sometimes be a challenging procedure. It's not always easy to pry the yoke away from the flange after it's been assembled for so long. We definitely recommend professional installation for best results, but for the strong at heart here's a brief explanation of how it's done: