I'm also in the 'depends on the person' park.
I would not sacrifice the people I love most just to save a thousand people I don't know.
I would sacrifice myself to save the thousand people I don't know, if this sacrifice wouldn't be too gruesome. Sepuko? Sorry; not going to happen.
Killing someone I don't know to save a thousand? Well; actively killing a human being isn't too easy. Absolutely not. It would seriously damage a part of myself. But I'd do it if that would save a thousand others.
Everything is relative. There's something called the Monkey Sphere; it describes the maximum amount of members of a given species that an individual, at any point in time, can honestly relate to as a fellow person. For humans, the average monkey-sphere size is 150 people. At any given time, the average human can identify with a maximum of 150 individuals. Anyone not in that number is outside of the monkey sphere, and we thus don't really, instinctively, see them as individuals. I know you are all individuals who read this, but that is rationally; not instinctively. You are all outside of my monkey sphere.
If the thousand people who are about to die are, at that point, outside of your monkey sphere, while the one person is inside it, you'll probably spare the one. However, if there are several people within that thousand who are within your monkey-sphere, you'll probably sacrifice the one, since there's more people within your monkey-sphere to save.
Behavioural biology is intriguing.
Did you know that sheep have a way larger possible monkey-sphere? They can remember 200 individual faces with ease, and their monkey-sphere might be as big as four-hundred individuals.
Another fun fact is that this hypothesis is actually answered in most pop-stories. Especially in the medieval fantasy genre, but also in mythology. An example of this is the war for Troy (Homerus). In order to save one person (Helena), the Greeks launched a full-out war on Troy.