greencard application question

Hi everyone:
I've heard some American people say that if you stay in the US for 10 yeras you can apply for a green card. I don't think the American people really know well about immigration regulations since they don't need any green cards. But I've heard quite a few American people say that. I know a lot of people here are very professional so I will take your words for the truth. Does anybody know if it is true that you can apply for a green card after staying here for 10 years? Or is it just another urban legend? Thank you very much.