let all who are hungy come and eat
The magid (in many ways the main part of the Pesach haggadah) begins with the following declaration: "This is the bread of affliction that our ancestors ate in the land of Egypt. Whoever is hungry -- let him come and eat. Whoever is needy -- let him come and celebrate Pesach!" (This is known as "ha lachma anya", for the opening words -- which are in Aramaic, the then-common tongue, so that they would be understood.)
I, and most liberal Jews I know, interpret this pretty broadly; we would invite a Jew or a gentile who expressed interest. Some traditional readings say this applies to a Jew only, pointing out that "come and celebrate Pesach" was originally about joining in the korban (animal sacrifice), which is only applicable to Jews. But (as someone pointed out else-thread), you must include your servants under most circumstances, even if they're non-Jews, so clearly there is some room for interpretation here.
I have a lot of readers who are learned in such matters, so I pose the question to you: whom do you feel obligated to include per "ha lachma anya", and who else would you include anyway? What are the issues?
Personally, I would include anyone who asked out of apparent sincerity, Jewish or not. I don't really care if the person is a seeker exploring Judaism or just curious; if he wants to learn enough to show up, he's welcome. The only bar would be to someone who has made it clear that his goal is to harrass, or who somehow poses a serious threat to me or my other guests. (That's hypothetical, but I include it for the sake of completeness.)
I am also mindful that I was that outsider once, that then-gentile who crashed a seder at the last minute because I realized it mattered. So there's some amount of "pay it forward" in my reaction, but it's not just that. I want to be the kind of person who says "of course; we'll just add a chair to the table", and the kind of person who is approachable in matters of religion.

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This had the effect of generosity in theory but it was an obviously token gesture, because the leader would immediately close the door afterward and sit back down.
If I'm hosting the seder I might invite a few folks whom I know moderately well and who seem interested. It depends. Since we share a seder with another family that includes three small children, the last few seders have been at their house (because we don't have to lug nearly as much kid-related stuff) and so I am hesitant to invite extras.
This year I did my Leukemia Fundraiser dinner in the middle of Passover (as it turns out) and I was very specific to say in the E-Vite that went to all the women in the neighborhood, "On Passover we say 'Let all who are hungry come and eat.' So I will be cooking for you."
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OK, the year Elijah really came to dinner was amusing... but it wasn't my house.
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My limit would be practical -- only so many people as I can shove around the table; only so many people as I can cook for.
Dunno how many that would be -- probably not more than, say, fifteen or twenty, if we used paper plates and dragged in card tables, and all that, and we'd probably have to serve something that tastes good but was on the less-expensive side. But I'd sure like to do that.
It might be a bit much for Lis, though, who gets peopled-out easily.
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The only /halachic/ Pesach obligations, as I understand it, are 1) eat matzah on Day 1; 2) Don't eat leavened foods for 7 days; 3) partake of a special sacrificial lamb (temporarily suspended); and 4) teach your children about this.
To reword my previous post: It is traditional to invite your entire household (including servants), whether they are Jewish are not, but men need to be circumcised to sit at the seder table.
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