I have the "friendly request." "Could I ask you to...It would help me a lot."
And I can do that with kids really well! Not quite sure how I learned it, but I can get a lot of kids to do something I ask. I think it's cause I speak to them directly, person to person.
And I can explain things ("when you fiddle with the tray table, it makes my whole seat shake--I bet you can't tell it from there, but it does. It's really annoying. So of course, you're going to need to put it up and down now and then, but I'd really appreciate it if you didn't fiddle with it more than you need to. Can I ask that favor of you?").
I've heard of the others, but what is the TootsNYC special?
I think it helps to count to 5 or ten before responding to something rude. It allows you go center yourself and also lets the other person's words just hang there in the air for a bit.
A blank look to something shocking works.
The TootsNYC special is named after a long time member of the forum here. Basically it's a way of dealing with an overly nosy person by turning the questioning back onto them.
I thought it was to always give the same response no matter how they phrased the question. It's a polite brick wall approach.
Maybe we need TootsNYC to referee 
I like to call it the "cut and paste"--basically, it's to answer a nosy question with either a non-answer or a simple answer, and then never deviate from the wording. (If you can be a bit funny, it's especially effective).
("Why aren't you married yet?" "Because Archie Goodwin is a fictional character"/"It just hasn't worked out that way yet")
So no matter where they take the question ("why won't you answer me?" "Aren't there any nice guys at your work?"), you just repeat the answer over and over. They give up eventually. In my experience, it takes about 4 times, maximum. But you cannot deviate, not the tiniest bit. The underlying message is, "This is all the answer I'm ever going to give you on this topic."