For example, my mom learned a number of years ago that she was the result of an affair her mom had. She did the Ancestry DNA test and a short time later was contacted by her half brother who had also done the test and was informed that he most likely had a sister in my mom.
Another family friend was adopted and she was contacted by a person who did the test and was told that our family friend was a cousin on her mom's side. She contacted our family friend and basically said, "I thought I knew all my cousins on my mom's side, but I don't know you." So our family friend was able to contact her biological family.
I think it is happening a lot now, and can probably generally be a great thing for these people. Also, as was told by chilango, there are many stories of people finding out their dad isn't their biological dad. As I like to say to my kids, "you're mommy's baby and daddy's maybe."