Are the people who live in your state predominantly people who were born in that state, or did they come from somewhere else?
Seth Kadesh at the brilliant Visual Statistix Tumblr has come up with this great visualisation which answers just this question, using Census data.
The redder an area is, the more likely it is that residents of that county were born in that state. The whiter an area is, the more likely it is that residents came from somewhere else.
Not surprisingly, parts of Florida, Nevada, Arizona and around DC are filled with people who came from somewhere else. Parts of Texas, Louisiana, and the upper-Midwest are among those places inhabited by original residents.
Also generally speaking, the Western part of the country is lighter than the Eastern part, suggesting that more people migrate West than the other way around.