I've seen two cross pin shafts fail, one sticking out of the diff cover like Mac's photo above.
One was on my friend's '67 Camaro, and the other was on my '68 Camaro a year later, on the same street within 50 yards of the same spot (irrelevant, but slightly interesting).
I recently found this on a Yukon blog:
Q: My cross-pin shaft is scored and the spider gears wore into it. What happened?
A: When a differential is traveling in a straight line, the spider gears remain motionless in the carrier. It is not until one tire turns faster or slower than the other that the spider gears rotate on the cross pin shaft. This most commonly happens when turning a corner. However, other situations cause the spider gears to spin much more rapidly, such as getting stuck in the mud or snow. When this happens, the spider gears can rotate on the cross pin shaft so quickly that it slings all the differential oil away from it, giving way to metal-on-metal wear. This causes the cross pin shaft and the gear to get so hot that they melt each other, sometimes to the point where they weld themselves together. Damage such as this can not only destroy the spider gear set, but compromise the carrier and ring and pinion set.
Hah! 48 years later, I finally discovered why our cross pin shafts failed. Open diffs and lots of extended power-wheel burnouts.