Hi BluErf,
I'll be interested for anyone to post measurements. Since I've been making staffs and canes for a while now, and reading about a bunch of clubs, I can give you the "it depends" answer now. Here's what it depends on, so far as I know:
Most weapons of any sort typically have handles less than 2" (5 cm) in diameter, simply because very few humans have a hand that can hold something thicker in a firm grasp. This includes things like sledge hammers and mauls, which can weigh 2-4 kg (5-10 lb) and have wooden handles.
Many clubs, staffs, etc. weigh between 2-5 lbs (1-2 kg, roughly), which, if you think about it, is the weight range of typical swords. I suspect that this is sort of an optimal range for weapons in general, being light enough to wield for an extended time, light enough to move dextrously, yet heavy enough to cause damage.
The basic point is that clubs seem to fall in the range of weights for all weapons, including axes, hammers, swords, spears, and maces. We seldom worry about handle failure in these tools, even though the handles are seldom more than 1" thick.
To give some idea about the relative strengths of woods, a yew longbow 1" wide and 1/2" thick would probably have a draw weight in the 50-100 lb range. a round "bow" that was 1" by 1" would probably have >100 lb draw weight for yew and for many woods. If you think of a club handle as a short, stiff bow, it looks like a 1-1.5" thick handle is thick enough to handle the forces its user would apply to it. Personally, I suspect that a club handle would only fail if there was a defect in the wood, due to rot, insect damage, or cutting across the grain of the wood. However, I would not recommend stress testing a century-old club, since wood does deteriorate with age...
My 0.02 cents,
F