Asked constantly, and rarely for the answer itself - the interviewer wants to know whether you can explain why.
The setup
Three doors, one car, two goats. You pick a door. The host, who knows what is behind each door, opens a different door revealing a goat, and offers you the switch.
The answer
Switch. You win 2/3 of the time by switching, 1/3 by staying.
The clearest explanation
Your first pick is right 1/3 of the time. That never changes - the host cannot alter what you already chose.
So the other two doors together hold the car 2/3 of the time. The host then removes a goat from that pair, which concentrates the whole 2/3 onto the single remaining door.
You are effectively being offered "your one door" versus "both other doors", which is obviously a good trade.
The assumption that carries everything
The host knows where the car is and always opens a goat door. Take that away and the problem changes completely.
If the host opens a door at random and it happens to show a goat, switching gains nothing - it is 1/2 either way. The host's knowledge is what transfers information; a random reveal transfers none.
Interviewers ask this variant specifically. Candidates who memorised "always switch" answer it wrong, which is the point.
The generalisation
With n doors: you pick one, the host opens n - 2 goat doors, and you may switch to the single remaining one.
Staying wins 1/n. Switching wins (n-1)/n.
At n = 100 the intuition becomes obvious - your original guess was a 1% shot, and the host has cleared away 98 wrong answers from the other 99%. If you are struggling to convince someone at n = 3, jump to n = 100.
Why it is asked
It tests whether you can reason about conditional information rather than pattern-match. See Bayes' theorem for the formal treatment, and practise in brainteasers.