Non-Answer

"This tells me less than nothing. Do you understand? You've made me forget things I didn't even know."

—Black Mage, 8-Bit Theater, Strip #1008

The Non-Answer is a response to a question that is so generic or vague that it's not really an answer at all. Usually, not only is the answer very vague, it is very obvious as well. This may be because there is no better answer, or the askee simply doesn't want to answer the question.

Compare Mathematician's Answer and Cryptically Unhelpful Answer.

Examples of Non-Answer include:

Anime

In Sonic X, Eggman once sent his robots to pick up an impossible amount of supplies from the hardware store.

Decoe: How are we supposed to carry all of this?
Eggman: With a great degree of difficulty.

In Naruto:

Naruto: Ero-sennin, how did you know that I have two kinds of chakra?
Jiraiya: Because I am a sennin.
Naruto: That didn't explain anything.

Film

In Fight Club, after the chemical burn scene, Marla asks what happened to the narrator's hand. Tyler has asked the narrator not to talk to Marla about him.

Marla: Who did that to you?
Narrator: A person.

In First Blood when Rambo is asked what he hunts with his huge knife, he responds simply, "Game."
In Dorm Life, Josh asks Danny B about his documentary:

Josh: So, uh, what'd you think about my doc, Dan?
Danny B: Uh, yeah, it was just the right length.
Josh: Uh-huh. But, uh, what about the content?
Danny B: Yes, it was there too.

Discussed in the Babylon 5 movie Thirdspace:

Sheridan: I will take your proposal under consideration.
IPX Agent: That's bureaucratese for F-off.

Literature

Karen Armstrong (IIRC) claims that the Biblical "I am that I am" is a Non-Answer.
- Similarly, some view "Thou sayest it," the answer Jesus gives to Pilate's question "Art thou king of the Jews?", as a Non-Answer. Does Jesus mean "Yep, you said it; you got that right," or "That's what you say; I never made that claim"? (Jesus Christ Superstar understands it in the latter sense.)
- "Render unto Ceasar the things that are Ceasar's and unto God the things that are God's", as an answer to whether the Jewish people should pay taxes to the Romans, is specifially stated in the Bible to be a Non-Answer. The questioners were trying to trap Jesus into making a statement either way, at which point they would either declare him to be a Roman sympathiser to the Jews, or declare him to be a Judean revolutionary to the Romans.
From Lemony Snicket: The Unauthorized Autobiography:

The stranger was a woman, at least as tall as a small chair and probably as old as someone who attended nursery school many years ago. She was entirely dressed in articles of clothing, and had nothing on her feet except a pair of socks and two shoes. ... [She] began to speak in a voice that reminded me distinctly of her own.

Live-Action TV

Lampshaded several times in Babylon 5, possibly due to the many times it was played straight, what with the Vorlons, and the Minbari, and Lorien...

Ta'lon: "While every answer is a response, G'kar, not every response is an answer."

Leonard Hofstadter's mother:

Beverly: Your uncle Floyd died.
Leonard: Oh my God, what happened?
Beverly: His heart stopped beating.

Buffy the Vampire Slayer, "Killed By Death":

Xander: You don't know how to kill this thing.
Buffy: I thought I might try violence.
Xander: Solid call.

- And in "Him"

Dawn: Last night, you said you weren't helping Spike out of pity. What is it [if not that]?
Buffy: It's a good question. (sips her drink through a straw)
Dawn: Is sitting there drinking soda some kind of a Zen non-answer?

On Lost, when Locke asks Ben how deep the Orchid station is, he simply says that it's "Deep."
Teal'c was a master of the non-answer in Stargate SG-1. For example:

Jack O'Neill: So what's your impression of Alar?
Teal'c: That he is concealing something.
Jack O'Neill: Like what?
Teal'c: I am unsure, he is concealing it.

Theater

In Hamlet, Polonius asks Hamlet what he is reading. Hamlet's response: "Words, words, words."

Video Games

Overused joke for MMORPGs, "What killed him?" "Ran out of Hit Points" (Not enough hit points, etc.)
- Similarly among medical types: "Cause of death?" "He stopped breathing" "His heart stopped" etc.
  - "Heart failure" is a legitimate answer to (almost) any cause of death. Of course, the real question is why the heart stopped.
Protip: To kill the cyberdemon shoot at it until it dies

Web Original

In Shadow of the Templar Jeremy is a master of this, as is Ethan.
(The Customer is) Not Always Right is full of these
The Shivah enables you to make almost every answer a Non-Answer by responding to every question with a question. To be fair, the point of your questions seems to be to make your interrogator realize the answer on his/her own... sometimes.

Western Animation

In Family Guy, Meg comes downstairs with a dress on, in preparation for a prom. She asks Brian, "How do I look Brian?" Brian says, not wanting to either lie to her or insult her, "Ahhhhh... You sure do, Meg."
Batman: The Animated Series used it in "Night of the Ninja." When Batman tells Robin that Kyotai is "good" at the martial arts, Robin asks how good he is. Batman reiterates, "Good." (Translation: "Better than me.")
Not in-universe (though there probably are several examples to be listed) but if you browse through the Phineas and Ferb wiki you can find the following 'information' about Ferb:

Age: Less than 15.
Height: Taller than Buford.

- How Phineas tells Candace that the Nose Lake Monster is real... she figures it out pretty quickly.
Arnold's bus pass is essentially this.

Name: Arn(obscured by thumb)
Born: Yes

Other

Jack Handey played it for laughs: "When my little nephew asked if the equator was a real line around the Earth or an imaginary one, I just laughed. Laughed and laughed. I laughed because I didn't know the answer, and I hoped if I laughed long enough, he'd forget the question."
Probably happened to you at some point: "Why can't I do X?" "Because I said so."
- Or;

Q: "How do I do [task]?"
A: "Very [adjective]ly."

Question: "What's For Dinner/What do you want for dinner?" Answer: "Food"
Rule 34 variant:

Q: "How do(es) he/she/they [[[squick]]y or improbable sex act]?"
A: "Very carefully."

Tom Siddell, creator of Gunnerkrigg Court, does this when he doesn't want to answer a fan's question.

Real Life

Real life example: when asked in one of the interviews what happened with Russian military submarine Kursk, Vladimir Putin answered "It sunk". (Which is also a grammatically incorrect non-answer, as he should've said "It sank".)
Real Life: When Willie Sutton was asked why he robbed banks, he reportedly replied "Because that's where the money is."
- More helpful than most, if you follow the logic train. "I want money." "Banks have money." "Thus, get them from the banks."
Another real life example: When famous moutaineer George Mallory was asked why he wants to climb Mount Everest he replied "Because it is there." (Mallory died on Everest in 1924, after may or may not reaching the summit).
Real world example: in Zen, the answer Wu or Mu, in Chinese and Japanese respectively, is a cross between this and a Mathematician's Answer. The original question asked was, "Has a dog Buddha-nature?" The answer loosely means, "Without meaning." A philosophical STFU to an Armor-Piercing Question. The Other Wiki has a better discussion for those interested.