In my tenth grade biology class, while we were learning about genetics, our teacher gave us an interesting take-home assignment. It was a list of genetic traits where the inheritance is relatively simple in humans--attached vs. unattached earlobes, curlable vs. uncurlable tongue, that kind of thing--and instructions to document which we had and which each of our parents had.
The awkwardness this might cause adopted kids, or kids who had no contact with one parent, was evident at the time and the teacher did kind of skate around it with a "well, just list your traits if there's, like, an issue." But I didn't realize until just now why else it might have been a bad idea.
"Mommy, if you're blood type A, and daddy is type O, why am I type AB?"
Whatever it is that you might find out about your family, that's a hell of a way to find out.