I live in New Mexico and bought house with a yard that is absolutely and totally completely infested with goathead plants (For those unfamiliar, here's what their seedpods look like--should be pretty obvious why you don't want them in your yard!).
After a week of heavy rains, here's what sections of the yard look like:
Pretty grim. Thankfully, they die in the winter, but not before growing little stickers to reproduce with that fall off and nestle into the dirt. So I think I may be able to kill them all off in a few years by simply killing the larger plants before they grow any stickers. Without a new supply of stickers, eventually the ones already in the ground should stop sprouting--I hope. Then again, they are perennials, so that may take a loooong time.
Does this sound like it will work? Has anybody else defeated a goathead invasion? I'd like to avoid poisoning the yard if at all possible because there's a lot of nice wildlife in the area. I anticipate living here for a while and can be patient about it, so I'd like to avoid simply covering the whole yard in plastic and putting gravel over it as many in the area do.