I was poking around on the Bureau of Land Management's General Land Office records site this afternoon. My Luxembourger ancestor came with a lot of siblings, and I was curious to find out how many of them claimed land grants. A quick check confirmed that my ancestor, his mother, and two brothers had all purchased land grants. Not ironically, the timing of their land grants corresponded reasonably well with their arrival in the area.
Which got me to thinking: if I didn't know my ancestors had been in the area, the GLO records might help me not only figure out where they had lived, but when they arrived there. This system isn't perfect - my ancestor never lived on his claims, nor did his mother - but it is a starting point. Besides, the GLO records just make interesting reading ;)