I use one of these: http://www.ebay.co.uk/itm/proops-Deuxieme-Gauge-bicycle-rim-gauge-0-72mm-bike-rims-measure-tool-/111647317689 to measure rim thickness. My recollection is that anything below 0.75 of a mm is dodgy (though I believe some of the very light rims are constructed with 0.75mm as standard!). Just checked, and Jobst Brandt took some of his rims to 0.5mm and wouldn't recommend it (http://yarchive.net/bike/rim_wear.html).
@benbrangwyn started
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I use one of these: http://www.ebay.co.uk/itm/proops-Deuxieme-Gauge-bicycle-rim-gauge-0-72mm-bike-rims-measure-tool-/111647317689 to measure rim thickness. My recollection is that anything below 0.75 of a mm is dodgy (though I believe some of the very light rims are constructed with 0.75mm as standard!). Just checked, and Jobst Brandt took some of his rims to 0.5mm and wouldn't recommend it (http://yarchive.net/bike/rim_wear.html).