hmmmm, I'm not sure, but quite a few. At least 3 broken ones that I can definitely recall, including one that I broke before I'd used it even once. I bought two now so I'd have a spare. With my luck, I'm never going to need the spare...
If I'd been thinking, though, I probably would have given up on hydrometers altogether:
-place the sample container (a graduated cylinder is perfect) on an accurate kitchen scale (the one you use for measuring out hops, +/- 0.1 grams is good, but the more accurate it is, the smaller the sample size needs to be)
-'tare' the scale
-pour in a measured sample at 'standard conditions' (i.e. 25 degrees C)
-simple math: 1.015, for example, means that 1000mL would weigh 1015g; or 100mL, 101.5g; or a 10mL, 10.15g (isn't metric fun?)
Easier, cheaper, and more accurate than your average hydrometer.