I don’t care much at all. What I’d really like to know is why my mom and dad never talked about their cousins, aunts, or uncles. Doing a family tree or delving into genealogy won’t give me that answer. A few years ago I got a FB message from someone in Sweden (my paternal grandparents and maternal grandfather were from Sweden) saying if I am indeed <firstnamelastname> relative of <maternal grandfather> then it 96% certain I am related to the King and/or Queen of Sweden. I’m surprised he didn’t ask for money to be sent in the form of a gift card…
I care less about things like my likelihood to enjoy cilantro and whether I prefer to sleep on the cool side of the pillow, and more about where my ancestors came from, and what they did with their lives. I plan on doing either Ancestry or 23 and Me sometime when it’s more convenient for me. See what I find 
Large parts of what’s now Italy were colonized by Greeks in ancient times.
Generations past can have a definite effect on the current generation. Here’s one example from my own life: one of my great-grandfathers was French-Canadian. He came to the Pacific NW of the US, possibly illegally, and changed his name rather transparently to its English equivalent. He spent most of his career as an itinerant cook at lumber camps in Washington State. His wife had an Irish-sounding name; possibly they were Catholic but I don’t know. They had a fairly large family, 6 or 7 kids that I know about. They were poor and uneducated, and their kids came out the same, including my grandmother, one of their daughters. This grandmother, still uneducated, was widowed at a fairly young age, when my father was 6. She knew nothing about child rearing except shouting and violence, and so that’s what my father learned. To give him credit, my father did not give in entirely to his background and upbringing, but the influence was definitely there. This, in turn, had its effect on me, and if I hadn’t been gay I still would have been reluctant to have children because I was afraid of being a bad parent.
I know nothing more about the background of these two great-grandparents. Sometimes I think it would give me a little more closure about my past to know what they came from and how they ended up the way they did. Or maybe not, it’s hard to say.
I find family history interesting because I learn history that way. Like how a several greats grandfather was court-martialed during the American Revolution, and got his sentence commuted because they were short on able bodied fighters. Or how his great grandparents fled from France because of the St. Bartholomew’s Day massacre. My own great-great grandfather was incarcerated in the notorious Andersonville prison during the American Civil War. Knowing these things helps the history stick in my head.
My brother died recently, and at his rather elaborate funeral they called out a list of his (and therefore my) ancestors*. The thing about Maori ancestors (tipuna) is that after a few generations you move from actual people to what may not have been real people to actual Gods. It’s quite a trip, and I’m not entirely sure how to reconcile it in my own head sometimes.
On my Mother’s side, all white European, there’s nothing of note. It’s fairly boring English nobodies forever and then we lose track pretty quickly.
All I care about is that my ancestors managed to survive and procreate. So they beat a gazillion others in the Darwinian lottery…my self is happy about that because I happen to be here to be happy about it.
That’s really cool. And now here we are talking about her on the internet almost a hundred years later. I wonder how her parents came up with that name.
Seconded! 
ie, not at all.