If someone say thank you in Chinese, how should you respond? Just as in English, there are many options ("no problem," "not at all," "it's my pleasure," et cetera). And just as in English, the "textbook response" is not always the most natural.
Consider the following possible responses
不 客 气 bú kè qi
不 谢 bú xiè
不 用 谢 bú yòng xiè
别 客 气 bié kè qi
别 那 么 客 气 bié nà me kè qi
不 用 那 么 客 气 bú yòng nà me kè qi
你 太 客 气 了nǐ tài kè qi le
你 客 气 什 么 nǐ kè qi shén me
别 和 我 客 气 bié hé wǒ kè qi
没 事 儿 méi shì ér
没 问 题 méi wèn tí
The first one is a standard textbook response. It's appropriate for strangers or acquaintances with a formal relationship. It might literally be translated as "don't be polite." In fact, nearly all of them mean something similar—a negative exhortation to the person who said "thank you." (The two exceptions are 没事儿 méi shì ér and 没问题 méi wèn tí. The first one can be translated as "it's nothing" and the second as "no problem.") The second literally means "don't thank." It's another textbook response, and it's the source of the common Chinglish "no thank you" in response to an English-speaker's "thank you"! The rest have varying degrees of formality.
So which one should you use? Of course it depends on the situation, but you should keep two things in mind. First, it doesn't really matter. Chinese people don't say 谢谢 xiè xie as often as English speakers say "thank you" (see below for more information), and when they do, the other person doesn't always respond anyway. (Or she might respond with a simple "mmm" or a nasalized 啊 ā ). Second, you will usually be fine if you just say 不用谢 bú yòng xiè. It's not too formal and not too informal!
A final note on thanking: 谢谢 xiè xie is not as common in Chinese as "thank you" is in English. But the reason isn't that Chinese culture is ungrateful or impolite—just the opposite. In China, thanking confers formality on the favor, almost like an official transaction of some kind. That's why it's weird in China for relatives or friends explicitly to express thanks to each other. For example, consider a typical American dinner table exchange:
A: Could you pass please pass the salt?
B: Sure. Here you go.
In contrast, it would be highly unusual to hear 谢谢 xiè xie at a Chinese meal (or 请qǐnɡ, "please")! This aspect of Chinese culture may be changing, and you might hear people thanking each other occasionally. But don't be surprised if people don't always express their thanks directly.