(plus discourse, of course)
Not exactly “non-famous” IMHO.
“You’d think Mama had never seen a phone. She makes no allowance for science. She thinks she has to cover the distance by sheer lung power.”
I’m probably splitting hairs - I’d define “non-famous” as being something that never got repeated / quoted much, that it never really made it into any popular cultural lexicon of any sort (probably because it was so darned long!) regardless that it could maybe be regarded as one of the film’s benchmark quotes.
Human Centipede? (never saw it and don’t plan to)
How about:
“It’s only a model.”
Monty Python and the Holy Grail.
Correctomundo, sir.
Nope. But I’ll give you a clue: It came out in the summer of 1966, and 11-year-old me thought it was well worth waiting seven months for. Watching it yesterday on cable, I couldn’t help laughing (and groaning) at it.
Fantastic Voyage?
Nope. It was the big BLOCKBUSTER of that summer. I’ll bet there was no one in the US who didn’t see it (or at least take their kids to see it).
Stumped for now. How about:
“My parents never divorced, although I begged them to.”
This should give it to you: It was based on what was the Number One TV series at the time.
Well, hoping I’m not the only clueless one still not catching on to that.
How about…which film did we hear the sung ditty “How much is that doggie in the window?”
(hint: possibly one of the most disgusting scenes in the entire history of cinema)
Batman?
Yep! With Adam West and Burt Ward.
Joker, Riddler Penguin, and Catwoman had a dehydrating machine they were planning to use on the Security Council of the United World, but first Joker tested it on some of their henchmen. They vanished into another universe when Penguin accidentally rehydrated them with the heavy water used by the Batcave’s atomic reactor.
Great fun, eh? 
BONUS CHALLENGE: Who played Catwoman in Batman: The Movie?
Lee Meriwether, of course.
Yep, “Miss Kitka.”
Still no takers for “You never had your hands on a teat before?”?
I’ll give you one more day, and a hint: it’s said with a (supposed) Plattdeutsch accent.
Stand By Me?
Nope.
Non-standard North German.
Was the speaker a Nazi by any chance?
Ha! No, quite the opposite, as this other quote by the same character demonstrates:
This gun of the hand is for the taking of human life. We believe it is wrong to take a life. That is only for God. Many times wars have come and people have said to us: you must fight, you must kill, it is the only way to preserve the good.