If I start a joke with a question, then answer it as part of a joke. What is the answer of the joke called? Is there a specific term for it? I am pretty sure there is, but can't remember what it was. Also, what if the main part of the joke isn't an answer? What would it still be called?
I'm not sure if it's the 'main' part (after all, the setup is just as important) but you're probably looking for the phrase punch line (also spelled as a single word punchline):
the sentence, statement, or phrase (as in a joke) that makes the point
It's often used for jokes which are like short stories; I'm not entirely sure if it applies to Q&A jokes as well (I'm not a native speaker).
The other part (which may be the long part, so it may count as the "main" part to some) is the Setup.
I found a Glossary of Comedy Terminology, if you have other humor-related questions.
I re-read and saw you were answering about the "punchline" area -- I think it's not so much that this second part is an "answer," but that it typically changes/challenges the audience's assumptions.
In the one liner: "Take my wife... please!" the assumption at the start is "I've got a good example about someone who does something stereotypical, my wife." But then with the "please!" it changes from an introduction to a longer section, to a direct, imperative command. Take her. Now. Make her go away. It's not pretty, but it's a change-in-direction, and that's what made it "work."
Some related terms from the Comedy Glossary that may help identify these parts of the joke:
Decoy Assumption - the misdirecting assumption in a joke's setup which creates the 1st story and is shattered by the reinterpretation.
Connector - at the center of a joke, the one thing perceived in at least two ways. One way of perceiving it constitutes the decoy assumption; the second way of perceiving it reveals the reinterpretation.
Shatter - with reference to joke structure, the point at which the audience realized that their assumption is incorrect.
Punch or Punch Line - the second part of a joke that contains a reinterpretation that creates a 2nd story that shatters the setup's decoy assumption.
Reveal - within the punch, the pivotal word, phrase, or action that exposes or presents the 2nd story's reinterpretation.
Tag or Tag Line - an additional punch immediately following a punch that does not require a new setup
As everyone else has said, the bit at the end that (hopefully) causes the audience to collapse in fits of laughter is known as the punchline.
If it's a more lengthy humorous story with lots of funny bits, but either a weak punchline, or no punchline, or a more serious point at the end treated lightly by what came before, then the whole thing may be a shaggy dog story, which Wikipedia defines as:
an extremely long-winded anecdote characterized by extensive narration of typically irrelevant incidents and terminated by an anticlimax or a pointless punchline.
Edit: I didn't properly read what Glorfindel said, but he's right. My bad, sorry.
I would say this is still called a punchline: https://dictionary.cambridge.org/dictionary/english/punchline
"The last part of a story or a joke that explains the meaning of what has happened previously or makes it funny".
It's usually what finishes off the joke and makes people laugh.
My first thought was "it's a call-and-response joke." If you wanted to go with that, your answer would be: the response.
I had a similar question, "what do you call this type of joke?", which led me here. I think I found the best answer to that buried in this fascinating Wikipedia entry which refers to this article, This Tablet From 1,500 B.C. May Contain The World’s First “Yo Mama” Joke: a riddle.
Depending on the context, you could refer to such a joke as a "yo mama," a "what do you call a this who that," or a "what do you get when you" joke. To get academic about it, you could go with an "interrogative," an "interactive interrogative," a "Q&A," or (to get ridiculously meticulous about it) a "Q&RQ&A" ("question, response question, answer") joke. For example:
Q: What do you call a person who comes up with a question similar to yours, uses it as a search string, finds this thread on StackExchange, and pounces on the opportunity to procrastinate?
RQ: I don't know, what do you [etc.]?
A: Obsessive compulsive!