For my first LARP Thing A Week, I've created a family tree for one of my NERO characters, Cameron MacDomnaill. I had some of it in my head already, but it was neat to take it out of my head and put it onto paper and into a computer.
This was actually a pretty useful character exercise, because it helped me create not only who his family members were (which is important to know) but also interesting things like how long his family usually lives (not too long, which probably defines them as adventurers).
In addition, it also helped me define something about the culture in which he lives. His connection with the clan cheiftains was going to be the typical patriarchal connection (his grandfather's brother was a chieftain), but I chose to make something new. The Adler chieftain is now chosen by his marriage to the female line AnAdler, a title which flows from mother to daughter. But the chieftain is still a man. This creates a new dynamic in the Adler tribe, as the AnAdler must necessarily wield some power and respect, but the chieftain is the consort of the woman holding that title.
Anyway, I encourage you to create a tree for your own characters. For some inspiration, I've included two pics, the ancestral line of Cam (my character) and the ancestral line of Riona AnAdler (the youngest AnAdler, who the next chief will marry), as well as a link to a web version of the tree I created on Mac Family Tree, a tool I'm already using for real-world genealogy.