I enjoy puzzles of all types - riddles, logic puzzles, magic cubes - and genealogy is a grand, endless logic puzzle specific to me.
It's interesting to find famous relatives and cousins to collaborate with, but it's a true joy to have a structure of a family that only you (to your knowledge at least) has looked at, puzzled over, and worked out.
In a way it's like other meaningless-but-challenging hobbies, ships-in-bottles come to mind, but it gives you insight into the lives of people that actually existed. These people that have been forgotten, but contributed a tiny piece to building your life.