Before doing anything drastic, like replacing your cluster, check the sender and wiring all the way to the speedo head:

There's a three terminal white nylon plug that slides over a circuit card edge on the rear of the speedometer itself. One wire supplies voltage to run the speedometer. On an '87, this is a red/black wire bringing unfused 12V from the ignition switch when in key position II.

The other two wires are, black (ground) and blue (sender). With the plug pulled (there may yet be an anti-tamper retainer) you can measure the continuity of the wiring to the sender and the sender itself. You should see about 3000 ohms measuring between the blue and black wires.

That test will eliminate 90% of what normally ails the electronic speedo circuit. The flexible wiring between the differential and the body, that plug and everything in between.

Also check to see the three-terminal connector is squeezing the card edge well enough for good contact. Sometimes, the whole problem is this plug falls off, or as vvpete has suggested, corrosion from a leaky windshield.
--
Art Benstein near Baltimore

my 1976 speedo died a while ago. i ordered a new speedo cable and now it works just fine. the problem is that the speedo cable attaches to the driveshaft right next to one of the mufflers. over time, the muffler gets the speedo cable really hot and warps it so it won't work. try that. it's not too hard.

Check the signal at the plug to the cluster. You can actually run the engine and drive with cluster removed. Alternatively you can jack up one rear wheel and let it spin. Some time ago I had a similar problem on my 88 740 which has the same set up. Had good signal arriving at the plug to the cluster from rear end but no speedo/odo action. Seem to remember that it was a problem with a bad connection inside the speedo on it's PCB or on the cluster PCB, can't remember exactly but it may have been associated with 3 prongs that connected when the speedo is mounted to the cluster. It was not a mechanical problem.

I used an analog meter to check the signal. It was an AC sine wave type signal around 3 to 6 volts obviously increasing in frequency with speed. Voltage went up a bit as well with speed.
--
David Hunter

I would make certain the connector under the floor, left rear of the car, is very securely plugged in. I've had them lose signal without actually unplugging. It's a weakness of that connector design.
Alternately, it could be a power problem in the circuit board of the cluster, or in the speedo head itself. Replacing the cluster is something you can do yourself with normal tools and a bit of patience.
Make sure to start with the steering wheel straight ahead, though!
Installing a used cluster temporarily will let you determine if the problem lies in the car or in the cluster. The speedo can be swapped out of the cluster as well - you can replace the whole thing or reinstall your speedo to another cluster, depends what you find to be wrong.
Note that the more common failure is that the speedo works, but odo doesn't- that usually means the plastic drive gear has self-destructed. Replacement gears are available if needed, but I don't think that's the problem here.

Good luck with it-
--
Rob Bareiss, New London CT ::: '87 244DL/M47- 230K, 88 744GLE- 220K, 82 245T-181K Also responsible for the care and feeding of: 88 745GLE, 231K, 87 244DL, 239K, 94 855GLT 189K

Yes, I actually did the odometer repair myself. I bought a used instrument cluster for $50 that had 142k miles on it and moved the odometer counter to the (approximate) setting of 262k miles, based on my logbook of gallons of gas used and average MPG over the last 5 yrs.
It's got to be two separate things, or a disconnect in the signal to the speedometer. The odometer gear can break, a common problem and easily fixed, but your speedometer should still work if this is broken. It must be the latter, a disconnected or grounded wire/connector somewhere.
There are several pins on the back of the speedo that can get corrosion. I would first pull it apart and re-connect everything with some electrical grease on the connections and see if that works.
--
'89 245 Sportwagon, '04 V70 2.5T Sportwagon