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I know of what I speak here. My first novel was born from my amateur genealogy research, and I have a second book from that material waiting in the wings. And yes, I am talking about fiction, not non-fiction.
Let me give you a quick example. During my research, I found out I have several female ancestors who came over from France to Quebec in the 1600s, as what are now called ‘Filles du Roi’, or 'King's Daughters'; these were women of good family and standing who journeyed alone across the sea to marry strangers, the men building up New France settlements. I’d never heard of these women before, and did some reading on them. But I had hundreds of questions about my particular ancestors: Why had they made this choice? How did their lives turn out? I could tell from the records who they married and how many children they had, but were they happy? Did they find love? Were they prosperous? So many answers I'd never know.
So I wrote my own answers. And stories were born.

But let’s pretend that you just have generations and generations of ‘boring’ family. They lived in the same village, same profession, had their families and lived unremarkable lives. That itself could easily be turned into an interesting story, say, the dynamics of several generations on the same farm; some people probably wanted to get away, some people probably wanted to stay. What would cause a family for so many generations to NOT change? And what did the family look like in 1600 vs. 1800?
Basically, think of the records you find as writing prompts; even an old box of family photos with people you don't know can do it. Can you look at a census record with a family’s information and come up with an interesting story around it? You probably won't be able to stop your brain from going wild, and even more so if you start fleshing it out with more context.
If you really want to build up your family tree for reasons other than just story inspiration, I’d suggest using something like Ancestry.com as your starting point. The site is easy to use, has a huge network of genealogists and trees, and a stunning array of databases (no, I’m not affiliated in anyway, I just love them). Of course, they do charge for that service, depending on how much you want/need to access. For software, I use Family Tree Maker, and I love it (this is paid software).
There are also free resources where you can make an excellent start, especially if you just want to give it a try and see how it goes:
My Heritage will allow you to search and build your tree on their site for free up to a certain number of people; if you want more, you pay. But if you’re a writer just looking to see what inspiration you can find, this is a good way to get your feetsies wet. They also have free family tree software you can download. And, they have a pretty decent section that will introduce you to genealogy and get you on your way.
Another excellent free resource is FamilySearch.org. This site is completely free, and they have an extensive database. There are two important things to know about Family Search, however. The first is, it’s not as user-friendly as Ancestry or My Heritage, although they do provide help. The second has to do with why the site exists. Family Search is run by the LDS Church (Church of Jesus Christ of Latter Day Saints, also known as the Mormon Church). They believe that the family of LDS members can be posthumously baptized in the church, and must be to get into heaven; because of this, family history research is an extremely important priority for them. When you create an account with them and/or build a family tree on their site, they can collect this information and use it for genealogical and Church purposes (you can see their privacy policy here). I don’t mean to argue this is a bad thing or a good thing, that’s a choice for each individual to make. I just believe I have a responsibility to let you know this if I'm suggesting the site to you. I personally am not a member of the Mormon Church, and am not endorsing it on that level.
Maybe you don’t want to know more about your own family—that can be a scary thing, and I get that. If so, you can always take a random trip through census records or other archives, and see what pops out at you—interesting names, strange family set-ups, odd professions. A great, free way to do that is at the National Archives; you can find the census page by clicking here, but there are other resources there as well.
One thing that both genealogists and writers have in common is the need to do a lot of contextual research, so it won’t frighten you when I tell you that you’ll probably find yourself googling all sorts of information about times, places, professions, and more. That alone can generate countless ideas! I’ve discovered professions I never knew existed on old census records, found inspiration in the look of church documents from the 1600s, and had ideas jump out when I saw how the topology of places changed with time.
So the next time you’re in a creative slump, try plugging some family names into the search engine, and even google, and see what you come up with. I promise you that before long your writer’s imagination will be off and running along lines you’ve never considered.
Happy hunting!
M.