In general, there is little overt discrimination in China against non-Chinese, except perhaps for persistent overcharging. But then again, many Chinese have the attitude that all foreigners (including ethnic Chinese from Hong Kong, Taiwan, and Southeast Asia) are moneybags, and will simply overcharge anyone and everyone they can. Ethnic Chinese, on the other hand, can use the "We're all Chinese after all" appeal for better prices, which the laowai (the somewhat condescending "old foreigner" term applied to non-Chinese) cannot do. Darker-skinned visitors may also have a slightly more difficult time of it than whites, especially outside of the big cities, but beyond the expected gawking and overcharging, those who don't speak Mandarin probably will not notice any difference.
On the other hand, once some sort of communication has been established, non-Chinese tend to receive better treatment from locals than the Chinese dole out to each other. Unfortunately, this situation sometimes even extends to Shanghai's top hotels.
The Ethnic Chinese Foreigner -- Ethnic Chinese who are born and raised outside China, but who do not speak any Chinese (and that includes any number of second-generation-on-down Chinese-Americans, Chinese-Britons, Australian-Chinese, and more) usually find themselves in an awkward position when visiting China. Simply by virtue of the fact they look Chinese, they are expected to speak the language, and those who don't are often viewed with a mix of subtle derision and exasperation. At the same time, they are not given the same benefit of the doubt as non-Chinese foreigners. While the reasons for this unfortunate phenomenon are age-old and complex, ethnic Chinese foreigners, like any foreign visitor, can go a long way in endearing themselves to locals by learning some Chinese and displaying some knowledge of Chinese culture and history. Even if you speak with a funny accent, the effort is usually appreciated. Learn the words for "We're all Chinese!" (Women doushi zhongguo ren!), and you may well find yourself paying a little more than local but a little less than foreigner prices for that special scarf. Mainland Chinese also tend to look very favorably upon ethnic Chinese foreigners "returning" to the motherland to search for their roots, a process known in Mandarin as xun gen.