If these are clinchers the most important thing to check is the brake sidewall thickness. The sidewalls will wear away over time due to brake forces and a sort of sandpaper effect where the brake shoes either contain grit to make braking more aggressive (the two most likely options both have a mild abrasives in their pads, Kool Stop or Zipp pads do not) or the pads can trap dirt and grit from the environment causing this to happen. If you mountain bike much, you may have split a rim from over ridding it, where you just sand through the sidewall and the thing pops open one day with a big circumferential split around the rim, this can happen on road rims as well, but requires less material removal because the tire pressures are much higher, and consequently tends to fail much more violently than in the mtn. bike scenario. The key thing to know would be what is the manufacturers initial rim width spec, and their minimum rim width spec. (if they have one) Most rims now have followed the new European standards and contain a groove or small hole in the rim sidewall that either wears away or shows through when the rim sidewall reached minimum thickness. Typically, the extra material in a rim to allow for wear is 0.010-0.015" (0.25-0.4mm) per side, so if your rim is more than 0.5mm thinner than when it was new, it's probably time to retire it, and if it is more than 0.8mm thinner than new, you should toss it (or get better health insurance).
This is still an issue on tubulars, but not nearly to the same effect due to the way the tire loads the rim.
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