The best times to visit are, hands down, April to June, and then September to October; there are few places in all of China that cannot be enjoyed during these months. You avoid the worst of both, summer (stiflingly hot and humid) and winter (biting cold). Popular opinion might suggest Chinese New Year as a great time to visit as well (February/March; the Spring Festival), but we recommend you check in advance, as most shops and local attractions will be shut, and hotels/transportation will be booked/sold out. Be sure to check the exact dates as the Festival follows the Lunar Calendar, and thus changes from year to year.
If you book in advance, then the Spring Festival (i.e. around the time of the Chinese New Year, February and March) is actually a great time to travel, weather-wise. But note that you are there only to celebrate the festival with a million other local Chinese; most shops and tourist attractions will either be shut or swarmed by holidaymakers. Summer months of July and August are also busy (as well as sticky hot and humid), so book in advance, and preferably stick to the northern regions for cooler temperatures. Head down to Hainan, aka the Hawaii of China to beat the heat on its beaches. Head south through the winter months of November to February; Hong Kong/Macau are gorgeous (and quite festive over Christmas), with just a light jacket and cardigan to see you through.
If you plan well, there is no low season in China, as such. Southern China is gorgeous (and can get busy) in winter (Hong Kong, Macau). The reverse is true for summer i.e. avoid the south and head up north, although even Beijing and Shanghai can get hot and humid, so pack accordingly.