I just went downstairs and took a caliper to some bows:
Craig Ekin Hill - 5/32" to 3/16" (Kind of rough leather made it hard to get accurate)
Ted Kramer Hill - 3/16"
Howard's Bow - 1/4"
Don't lose site of the fact that this here is art as much as science and is going to depend on the hardness of the wood, the sharpness of your rasp, how much sanding you do, the shadows in your shop and how healthy the animal was whose hide you're lining the backplate with.
Correct theoretical answer is probably Craig's 3/16", though I do lean awful hard on checking back to my Howard when in doubt. I think the competition standard is minimum 1/8". Practical answer is probably "'bout that much plus a bit, a smidge or a frog hair, dependin'"
My own vary from a slim, barely legal 1/8" to 13/32" on my classic that has no shelf at all. I tend to vary them some in proportion to draw weight, too. Probably need to set some standard but that'd take the fun out of it :^)
(Sorry for being flip, but I haven't had my coffee yet...)