Alternative and related questions:
What newspaper do you take and why?
Do you know what the current news headline is?
The meaning behind the question:
This question is closely linked to the next question we'll be covering, "Are you interested in current affairs?" and could be asked either before or after that question. In asking what newspaper you take, the interviewer will certainly be aiming to establish if you are interested in current affairs but they'll also be discretely probing your values. What newspaper someone reads can often say a lot about them.
Your answer:
This can be a surprisingly difficult question to answer. Common wisdom has it that the newspaper someone reads says a lot about their political, intellectual and even class values. What images spring to your mind when you think of readers of the following newspapers: The Guardian, The Sun, The Independent, The Telegraph. They each conjure up a very different kind of person, don't they. The question you have to ask yourself is what kind of a person you need to be!
You're certainly within your rights to simply tell the truth and you're also within your rights to tell the interviewer what you think they might want to hear (although guessing what that is can often be tricky!) In all cases, though, you'll need to be prepared for them to ask you why you choose that particular paper. But I'd suggest avoiding the tabloids; it makes for an easier answer.
By the way, just in case you were wondering, telling the interviewer that you don't read any newspapers isn't going to reflect well on you. Conversely, reading more than one newspaper is of course perfectly acceptable.
Example:
I read The Independent. I recognise that all newspapers, The Independent included, inevitably have various editorial biases but I feel The Independent gives a particularly well-balanced view of the world and what's happening in the world without having too much political bias. I also check the BBC News website each day. Between them, I believe I'm getting a reasonably well-rounded insight into current affairs.
Word of warning:
The obvious follow-up to this question is for the interviewer to ask about an issue or, if you're unlucky, a specific article that has recently taken your interest. Just make sure you're ready for that!