Not much wearing out as much as rattling loose for me. I'm running a couple of old stihls, an 051 and an 075. In 15 years of milling I have toasted an ignition coil, a rim sprocket, and an oil pump. The oil pump didn't fail as much as it just wore out from use.
As for rattling loose I have lost 1 bar nut and a couple of other assorted nuts and bolts. Loctite is now my friend.
I use a grandberg mill and I wear out the bar clamp bolts and the U bolts that adjust the height. I switched to grade 8 nuts so the wear is primarily over streatching of the bolts.
I cary a few 5mm bolts, a couple of cariage bolts for the bar clamps, a few nuts, a spare air filter and chain and thats about it for spare parts. I do have a couple of extra carburators and if I am traveling a long way I try to remember to toss one in the tool kit just because it is easier to change carbs than clean the screen when in the field.