I find it absolutely fascinating.
I suddenly got the urge to start researching it after my grandmother died and I regretted not having asked her more questions while she was still alive. I now know far more about her ancestry than she did.
I know that a lot of things we previously believed about the family weren't true. For example, my grandmother's father was Australian and we all thought their whole family had been wiped out in the Spanish flu epidemic and the sister he had been visiting in London when he met his wife was the only family he had left. I've since found out that he was actually the youngest child of a Jewish/Christian couple who were both cut off by their parents for not marrying within their own religion, that they went off to Tasmania and had six children before finally marrying once their parents had died, and that the children were eventually dispersed between Australia, South Africa and the UK but kept in touch and even visited each other fairly regularly despite being on three continents and it only being the turn of the 20th century. As far as I can tell no one died in the flu epidemic. My grandmother's mother was supposedly Welsh but I now know that she actually had no Welsh blood at all but was the child of a cockney and a very middle class German who went to London to make his fortune. I still don't know what happened to him because he disappeared off the grid (his wife then went to Wales and married her third husband, almost certainly bigamously), but I've managed to trace his ancestors back for centuries in Germany.
I don't know why I find it so fascinating. I think part of it is that I would love to have been a detective and this is a very satisfying way of solving mysteries without committing any crimes or putting myself in danger! I can spend ages obsessed about finding out more about a particular branch of the family tree and I find it so satisfying when I have a breakthrough. I suppose the likelihood that some of these people somewhere along the line were not actually fathered by the man named on their birth record, and so they aren't actually my real ancestors, is fairly high. But I don't tend to think about that.
When researching family history in the last 200 years or so there's often enough information to put together a fairly detailed picture of how these families lived and what happened to them. For example, my great great great great grandmother gave birth to stillborn twins and then married less than three weeks later. I don't know whether her husband was the father of her twins or whether her parents took advantage of the fact that her babies had died to get her quickly married off to someone else. But when I think back to my own wedding day, I can't imagine how different it must have been to get married when you're still an emotional and physical mess from giving birth to stillborn twins a couple of weeks previously. She then had another stillborn daughter and then a son who only lived seven months, at which point she and her husband moved to the other end of the country. I imagine her as a 30 year old woman who had given birth to four babies and yet was still childless, wanting a fresh start and moving to a completely new place. She eventually had at least three surviving sons, but no more daughters as far as I can tell. I wonder how she felt about not getting to raise a daughter.
These are all stories of people whose lives were just as interesting as mine is to me, and learning about them means they aren't forgotten. Sometimes they were forgotten but my research has in a way brought them back to life again, through random records uncovered in improbable corners of the internet.
Then when you get back to even earlier generations, it's mostly just baptisms, marriages and burials, but it still gives me a thrill when I manage to go back one generation further and tell myself that this person with this fairytale name (Maudlin Grimault, anyone?) I found in this very old book in almost indecipherable script was, unless someone had an affair with the milkman, one of my direct ancestors.