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I have an 85 zx9 that recently started feeling like the rear wheel would "shift" or move. Sort of felt like it would if in a power slide, but not as drastic.
All the rear suspension was tight, i.e. swing arm, axle & adjusters, etc. I tore it apart but can't find any obvious wear & tear. Before tearing it down, I was looking for any slop in the rear wheel. The only movement I got at the wheel was forward & back. (Not right I assume) No slop side to side, up & down, just straight forward & back about 1/4 - 3/8 of an inch.
There is slight movement @ the tie rods while off the bike w/the connecting bolt finger tite. As I said I can't find any obvious wear, no dry or damaged bearings or seals, pivot bolts seem straight, no gouges or wear marks.
I'm lost. The "crossing up" sensation I was feeling wouldn't come from the front end would it? Any help is greatly appreciated.

What condition is your rear tyre in?

If the rear wheel moves 14-3/8 inch in any direction, you have wear either at the rear hub/axle or at the swingarm bushings where it attaches to the frame. This could cause a bit of an unhinged feeling in the bike. SO could sloppy stearing head bearings or front hub/axle. Give everything that turns a few good hard tugs and see if you have any more movement someplace.

Since my last post, I've checked & re-checked, had friends look to see if I missed something. The only thing I've found is some slight "wollowing out" of the foot peg bracket holes.
Would this cause or be the result of the rear wheel feeling like it's "steping out"?
This problem has me perplexed. It doesn't do it at any certain time. Under power, cruise, turning it comes & goes. It's fairly un-nerving @ 80 mph or more, but it's noticeable @ 40 mph also.( Just @ 40 mph there's no "bites" taken out of the seat like @ 80.)
The rear tire is probably around 1/2 tread life or better, the front tire is 3 months old & matched in series & make to the rear tire. I'm not rough on the bike, i.e. burn outs, wheelies, etc. I'm especially easy on it w/the wife on back. I'm not holding up traffic but I'm no GP Moto rider either.
Has anyone else had this problem or is it just because it's a 20 year old bike & needs to be put to pasture?

I had that feeling with my bike in a nice long sweeping turn, most disconcerting I'd
say. I could find nothing wrong back there so I took it easy until I reached the next
gas station and re-checked the tire itself. Yup, way down on the air pressure... topped
it up and was fine for the rest of the ride.

Yes I made sure to re-check it in the morning when it was cold and had to top up the air
again...

get a mirror and check every weld on the frame for cracks they are hard to find--look for rust at the welds this is usually a clue to a crack.

Checking over your frame is not a bad idea at all. Your shock my be shot as well, wouldn't hurt to get it checked if nothing else shows itself.