See also the series of articles beginning with The O'Rourke y-DNA Results.
My sister recently tested the autosomal DNA of a cousin on our mother's side. A person inherits autosomal DNA from both their mother and father, unlike y-DNA which comes only from their father. Autosomal DNA is useful for finding reasonably close relatives, up to third and fourth cousins.
Why would you want to do this? Well, your third cousin is descended from the same great-great grandfather as you are. This isn't as far back as it sounds, as you will see from the examples.
Also, maybe that is as far back as you have been able to trace your family, but the third cousin that you locate has been able to work back farther. This could help an American family locate the place their ancestor emigrated from, say in Ireland or England.
Here are a few of the top matches from the DNA we submitted. FamilytreeDNA estimates that they are third cousins to my cousin:
So you get the idea.
What I didn't find anywhere near the top of the list was anyone named O'Rourke or Rodgers. There were a few, but they were ranked pretty low when sorted by likely matches, how much DNA you shared, etc. Likewise for people who said their family was from Leitrim. That is where the large O'Rourke clan in Ireland was based at one time.
If you need any help understanding all this, maybe this formula will help you. It comes from the Wikipedia article on centimorgans, which have something to do with it all:
Pr[recombination|linkage of d cM] = sum_k=0^infty Pr[2k + 1 crossovers|linkage of d cM] = sum_k=0^infty e^-d/100 frac(d/100)^2,k+1(2,k+1)! = e^-d/100 sinh(d/100) = 1 - e^-2d/100/2
Didn't help you? Me neither.
Continued in The Carsons and the O'Rourke DNA.
The image of a DNA strand comes from Wikipedia:File:DNA orbit animated static thumb.png.