We're a bilingual household in a country that speaks a third language. I speak Finnish to the kids, my wife speaks Japanese, and I speak Japanese with her.
Our older son recently started going to preschool, so he's picking up English at an expected-but-still-astonishing rate. He occasionally tries to speak it with me, in which case I pretend not to understand until he switches to Finnish, and my wife does the same for Japanese. So far so good.
But now he's also started speaking English to his younger brother, who's not yet verbal but will be soon enough. Uh-oh.
Now I realize that English will be their primary language (as long as we stay here), and I'm totally OK with that, it's my strongest language as well. However, I would like them both to have a decent grasp of their parents' languages, so I'm not too keen on 'unnecessary' English in the house; unlike this question, my wife and I never speak it at home.
So: should we enforce a "no English at home" rule? If yes, how and to what extent (eg. at dinner table, when talking with both of us, even when it's only the two of them), and if no, why not? Extra points for links to actual research.
Update: To expand on this a bit, our children have three passports, and it's entirely possible that we'll move to another country (with a fourth language!) at some point. Our short-term goal is to make them fluent enough to talk with their grandparents; and longer term, that they can realistically study/work in any of those three countries when they're old enough.