On my old '84 DL wagon (286+k, automatic) I found that the rear axle shafts have, what seems to me, a LOT of end play. How much should there be and how much is too much? (My dial gauge is at work so I don't have an exact dimension on how far it is moving).

Not sure, but when the end play gets to be too much, the rotor will ride on the outside brake pad too hard and the car will grind to a halt. At least that's what had happened to a car my son bought. When we took it apart, we found that the bearing had disintegrated and fell out in little pieces, the axle had tried to come out of its housing, and, luckily, the caliper was there to stop it.
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Thanks everyone for all the help, Doug C. 81 242 Brick Off Blocks, turbo bars and wheels, M46; 86 244, B230, 155k , auto; 81 242 Turbo, intercooled, M46, 122k; 93 245, B230, M47, 153K.

I don't know the specification, but a surprising amount is tolerable.

My '91 with 220k mi had nearly 1/8" of play when I decided it was time for new axle bearings. The bearings looked perfect when I took them out. The new bearings are much tighter, but there is still perceptable play.