Family (hi)story
My enthusiasm for undiscovered truths (or speculative assumptions, whichever appeals most to my romantic imagination at the time) led me a few years ago into family history. Gather up a list of names, dates and occupations, add some knowledge of the area, and the traits they passed down to you, shake it all up with a dash of imagination, and hey presto, your very own War and Peace.
I'll never know for certain how my ancestors spoke, what they wore or ate, how they felt about each other (or about the wider world) or whether I'd have liked them (probably not, for the most part), but fleshing out their lives provides me with some entertainment and mental exercise. It's a study of characters and their motives; if I write a character and I need him to end up in Paris, I have to ask why he would go there and in what circumstances. The same applies when you try to decide why Great Uncle Herbert moved 200 miles and became a miner instead of a watchmaker - there's no right answer, but there might be a satisfactory one. I don't actually have a Great Uncle Herbert, by the way, though I do have plenty of miners and a couple of epic moves, despite OneMonkey's firm belief that my entire family came from one village and are as inbred as you can get.
Of course, there's a danger of letting your imagination run away with you, of reading motives where there are none, and applying modern reasoning to an eighteenth century situation, but since no lives or fortunes rest on my research, it doesn't really matter. I often wonder about the difference between my interpretation of the evidence, and the actual truth as it happened, and I wonder if my ancestors would be shocked, amused or annoyed if they knew what conclusions I'd drawn.
This idea of logical but wildly incorrect conclusions from historical evidence gave me some story ideas, none of which have been developed very far yet, but mainly play on the reader knowing more about the past than the central character doing the research, so they can see the way that character reads their own personality and desires into the evidence and misinterprets it. It's not exactly the most original theme (and I probably got it from Possession by AS Byatt, which uses a similar idea in the context of academic research in English Literature), but I was still put out when I started to read The Virgin Blue by Tracy Chevalier. I won't spoil it for anyone but it plays on the idea of a modern-day researcher delving into her family history, and interweaves the story of her sixteenth-century ancestors, showing the patterns and repetitions in history. It's simultaneously encouraging and disappointing, to find that an idea similar to my own has been used in a popular novel, but I suspect it was published because Tracy Chevalier was already well-established, and not because it struck anyone as a great idea.