I do not think that they should. It is googles choice if they want to sensor what they are putting out there as long as it is not classified information or something like that. I do not think that google would have access to the type of information that our nation would not want China to have.
Censoring Chinese searches is unfair and detrimental to the people of China. A government that regulates information is very dangerous. People have a right to know exactly how their government is behaving and operating. The truth can be bad, but people should have the right to know it. Censorship is a bad thing.
It's not the job of a private business to censor itself. Chinese citizens should be allowed to purchase Internet filtering software approved by the Chinese government in order to prevent its own citizens from viewing objectionable material. The Chinese government's censorship on any level is wrong. However, it isn't up to Google to pander to the government. Google may placate the Chinese simply because it's a huge economic market, but it doesn't make the issue any less wrong.
I feel that Google should stand up to Chinese officials who want the company to censor its search results in the country. The free flow of information is a necessity for a functional society, and the clamp down by the Chinese government is yet another way that the Chinese are attempting to keep their citizens down.
Much like China's one child only policy, this should not be a debate. Google's censorship of search results in China is wrong, flat out wrong. Everyone deserves access to any information they may want freely, no matter if it's good, bad or somewhere in between. Neither the state, or companies like Google should be able to infringe upon that right to information, be it in China or anywhere else. So no, Google should definitely not be censoring search results in China.