I'm restringing my sister's guitar and the bridge pins keep popping out when I wind the tuning peg and tighten the string.

Am I doing something wrong, or are the bridge pins just peices of crap????

You probably are just not pushing them in hard enough. The pin wedges the ball on the end of the string over to the side of the hole through a slot in the pin, or if it's a solid pin it wedges the string over to a slot cut in the bridge. Read the bottom of the article I sent about "Flying bridge pins".