Hey there! We have gotten a lot of comments about steering wheel shaking and I'd like to toss out my rules of thumb on the matter based on my experience. The following can certainly apply to any car, but in particular my experience is in FWD cars.
 
Shaking steering when...
 
...you ACCELERATE = an axle problem, usually caused by worn CV joints or possibly an axle balance issue. In highly worn axles a slow "walking" of the wheel back and fourth while going straight at speeds under 10-15 mph can be noticed, but this may be dampened by power steering systems. Another sign an axle is bad would be noises like knocking or rattling when turning in tight circles at slow/med speeds. Since your typical transaxle halfshaft is not long enough to really exhibit a balance issue we recommend replacing the axles with new or rebuilt units.
 
...you COAST = a wheel balance issue, which can only really be truly diagnosed at 60 mph or higher. It can be noticed at slower speeds, but it may not appear or be obvious until 60. However if it does not appear at 60-65 mph, there is a good chance the car does not have a balance issue. First, make sure the tire pressures are accurate. Stick-on weights can fly off the wheel causing this issue. As tires wear (even or uneven) they can throw off the wheel balance as well. Sometimes well-wearing tires may need a rebalancing before they actually need replacing. We have also seen balance issues occur at minimal speeds in situations of juvenile joyrides. Off-roading after rain will cake wheels with mud causing severe balance issues. Less common but also possible issues of coast-shaking include wheel damage like denting or gouging, and tire damage such as tread delamination and sidewall bubbles. To test for a bad tire that might be causing a steering wheel shake, rotate the front tires to the rear to see if the vibration moves from the steering wheel and into the chassis.  
 
Alternative to the vibration while coasting issue would be a bad shock absorber, which would be accompanied by extremely poor handling and potentially odd "skipping" tire wear.
 
...BRAKING = a rotor or pad wear or warping issue, which is covered extensively in the Brakes Technical Section of this forum. For the most part these vibrations must be experienced under braking from speeds over the 60 mph marker. Vibrations at lower speeds than this are usually rotor warping issues and one can feel the brakes sequentially grab and release with consistent, light pedal pressure. Pad deposits formed unevenly on the rotor surface can cause vibrations usually at higher speeds, and heavy braking maneuvers or rebedding can sometimes remedy the problem, and if it does this can be an indicator that the driver should try using different brake pads more suited to their driving style. Vibrations in the steering wheel indicate a front brake problem. A feeling of vibration in the car's body or the seat of your pants usually indicate a rear problem. Pulsation in the pedal can be inconclusive as to front or rear issues while either or both of the issues can exist. To test a rear brake shimmy, apply gentle pressure to the e-brake while coasting without touching the pedal. A rear wheel vibration will be apparent then.
 
Heeltoe does not cite alignment issues as cause for steering wheel vibration. Alignment problems cause pulling, poor handling, and uneven tire wear which can effect wheel balance, but a bad alignment itself will not manifest in shaking.
 
Also, wheel bearings will not cause vibrations until they are so worn that the noise inside the car will be blatantly obvious. A wheel bearing can be heard long before it is felt.
 
Aside from these rules of thumb one should not consider that other problems can exist. Aftermarket wheels which are not hubcentric and do not have hub rings installed can cause vibrations in numerous cases. Also loose suspension bolts can be problematic as well. Shaking accompanied by clunking or clanking or other noises should definitely be checked out immediately and closely!
 
Marcus