Two popular fixes: West System has instructions for injecting an epoxy-silica-graphite mix into the shaft log, and placing shims.
Both are discussed in this thread, among others:
http://www.ericsonyachts.org/infoexchange/showthread.php?1737-E38-200-Rudder-removal-bushing-replacement
Clunking in the steering while sailing is bad, but a little play noticed when grabbing the rudder on the hard is livable if you don't feel it under way.
Also check the top bearing under the cockpit deck. It comes loose, is easy to tighten, and can feel like lots of bad things.
The WestSystem epoxy fix is a bit scary if something goes sideways. There was a guy on the east coast who did it on his Catalina 30 and, it appears, failed to adequately prep the rudder post with the release agent so it would release from the epoxy. He actually glued his rudder in place! :0 With the help of a friend of mine, who designed a tool that allowed him to put a large amount of torque on the rudder post without flexing the rudder from side to side, he eventually managed to break it free but not without a lot of serious agony. If you were to do this fix, make darn sure you prep that shaft so it will release without any doubt. But more to the, point, I don't think the WestSystem fix really makes much sense anyway. For a rudder post that is simply coming up through a fiberglass rudder tube, the post only bears on the bottom (where it exits the hull) and the top of the tube. Pumping epoxy into the tube will only add friction to the center portion of the tube to no good purpose.
In fact, when I replaced the rudder on my E26 (due to a bent rudder post from the P.O.), I had Foss turn the center of the shaft on a lathe to relieve slightly the diameter of the post's center portion in order to make sure there would be no friction against the center portion of the fiberglass tube. (The amount of material removed was not huge, and at any rate I went with a larger than normal wall thickness on the new rudder post, so it's still quite a bit sturdier than the original one.)
So what you need to do is eliminate the play at the top and bottom. This can be accomplished by shims. Some suggest mylar shims, but I used stainless steel shims I obtained from McMaster-Carr. Because they come in a variety of thicknesses, I was able to dial in the exact thickness I wanted and eliminate the play without adding unwanted friction. I figured out the thicknesses I wanted through trial and error--thicker in the bottom than on top, as it turned out. For the final step I dropped the rudder, greased the rudder post, and then reinstalled the rudder with the shims in place top and bottom. It still works great. At my haul out in June I'll go ahead and drop the rudder to give it a fresh coat of Teflon grease, reinsert it, and call it good.