Goatheads- I never heard this word until I moved to New Mexico. In Jersey we just call them stickers. But out here, they do look like little goat's head. And you know when you've stepped on one. OUCH! They will even go through some soles of shoes.
Even after you remove it, there's a lingering feeling that it's still there. I hate those things. If your not careful you can bring them in the house and then your pets step on them. (My poor dog).
I have learned to scrape my shoes before coming in the house or, take them off.
I found the best way to get rid of them is to pull them with gloves on your hands, by the root, before they get the little stickers on them. They pull up very easy if you get them before they flower. Once you pull them out they shouldn't come back. It takes time if you have a lot of them. If it rains, they will spread.
Talking with my neighbors and people who have lived here a long time, this is the only way to get rid of them.