For the past few months, my car has been acting like one of those vibrating massage machines while travelling at 60 or so. I brought it to my mechanic who balanced all the wheels … no effect. So I brought it back and left it with him for a day so he could check things out. Alignment was good, and he found nothing mechanical to cause the vibration. He wanted another crack at it so I left it another day. He tried moving the wheels around and rebalancing with no success. He told me that the only thing left was wheel slightly out of round, and that since my tires were not top of the line, it was something to suspect. I brought the car to the tire place where I had bought the tires a year ago and related the story. He looked at my tires and notice the signs that one of them had gone flat at some time (it had), and that it might be causing the problem. So I told him to go ahead and replace it. An hour and a hundred bucks later, I drove out of the tire shop and onto the highway and was again given a massage 
What now? Do I have them replace the rest of the tires? If it doesn’t fix the problem, I’m out the cost of the tires. Is there something else that should be checked before I have the tires replaced?
Yes, it could be those “not top of the line tires”, especially if a belt has shifted in one of them.
However, this could also be caused by bad bushings in the suspension, or by worn-out suspension or steering components. Since you did not bother to tell us the odometer mileage or the model year of your Saturn, we don’t really have much to go on here.
It’s a 2003 with about 75000 mi. on it. I will ask my mechanic if he already ruled those possibilities out, thanks.
I’m thinking my plan should be to replace one tire at a time if the dealer goes along with it.
Do you feel the shaking in the steering wheel mostly or is it in the seat of the vehicle?
How many miles on this car? Has anyone considered the possibility of a worn tie rod or tie rod end; or even an engine performance problem?
Thanks for the reply and sorry about leaving out the mileage - 75000 mi.
It’s more in the seat than in the wheel, although I do feel it in the wheel a little bit. The passenger seat back vibrates quite noisily. I can record it if you like … 
I’ve tried racing the engine in the driveway with no symptoms but of course that probably does not rule out an engine problem.
90% of the time, it’s a bad tire, tread separation or broken belt. This is usually discovered / verified during balancing…So is a bent or out of round tire or wheel…You can see these things…Since you have have bought ONE new tire, (not a good idea) you might as well buy 3 more…But everybody here, including me, are just guessing…
I feel for you, I have the same problem with my 02 SL with 213k miles. It started around 180k. At first it was mild and occurred between 58 and 62 mph. Now its much worse and occurs between 58 and 65-70. I have balanced, replaced and rebalanced the tires. First tires were Bridgestone Turanza’s, now Michelin Hydroedge. I suspect the wheel bearings but I’m going to look at the disc rotors too as I replaced them right about the time this started.
I think you have multiple things going on - and if memory serves me correctly, this vehicle is one of the most vibration prone vehicles ever made. That may make fixing all these problems difficult and expensive.
First step: Find someone with a Hunter GSP9700 Road Force balancer. If there is a tire and/or wheel problem, this unit is 99% likely to find it. Tell the operator he should be looking for very low values - under 10#.
Once you have eliminated tires and wheels, you can start on the rest of the vehicle. Be aware that on this vehicle some kinds of vibartyon issues are going to appear just like a wheel end vibration - and they aren’t.
I agree with Capriracer that you should find a shop that does road force blaancing. It spin balances the wheels with a simullated road force applied via a spiinning drum pressed against the tread. Thes machines can detect tire defects and anomolies that other machines cannot.
I also agree that in the overwhelming majority of the cases when all else is in good condition these vibrations are caused by tire anomolies.
First of all, thanks everyone for your replies. I certainly appreciate that all anyone can do is guess about this, and the last thing I expected was to hear someone say "Hah! I know exactly what your problem is! It’s … "
That said, the comment about the disc rotors does resonate. I did have the brakes overhauled last Jan or so, so the timeframe seems to be right. What is it about the disc rotors that you suspect could be causing this vibration? Would it be a “bad” rotor, or would it be something that could be corected by having the rotors turned?
If the vibration takes place while braking at highway speeds, that is an indication that the rotors are likely to be the source of the problem. However, if the vibration takes place while simply motoring along at high speed with no brake application, the brake rotors are not a part of the problem.
Nothing that you have provided to us so far gives any indication of the vibration taking place exclusively when you use the brakes. Under what driving conditions do you feel the vibration?
Is it only while braking?
Is it while driving without brake application?
Both?
Some clarification is needed here.
Brakes not applied at all, so there goes that red herring. Sigh.
However, keith’s description of the symptoms is right on. The vibrations initially appeared only between 58 and 62, and over time (and perhaps as a result of some of the attempts to correct the problem) have steadily worsened so that they now appear between 60 and 75. Vibrations occur whether accelerating, coasting or decelerating. What’s reeally maddening is that sometimes they stop for a minute or so and then reappear without any rhyme or reason.
Okay, so you can definitely forget about brake rotors being connected with the problem.
The fault lies either in the tires or in worn/defective front-end components. Since bad tires and bad front-end components are real safety issues, I strongly suggest that you take the car to a different mechanic who will–hopefully–have the expertise to locate the source of the vibration.
As has been suggested already, beginning with Road Force Balancing is a good place to start. If that does not help, then you have to move on to finding what parts in the suspension or steering are worn out.