There are a few numbers of Chinese dialects apart from the official mandarin Chinese (or Putonghua based on northern Chinese dialect): Cantonese, Wu, Min, Hakka, Gan, Xiang, etc.
Dialects or Languages?
Chinese language is the language spoken by most people of the world, at least theoretically. There exist many inhabitants of China, especially in the South, that do barely understand the official language that is based upon the dialect of Peking. There are a few numbers of dialects, or we should better call it languages, in China that are related to the official language. These dialects are more archaic than the modern official language and tend to have more tone pitches and closed syllable endings. The most important languages are:
* Cantonese Guangdonghua 廣東話 or Yueyu 粵語, spoken in Guangdong (the origin of the city name Canton is actually the province name, the city is called Guangzhou)
* Wu 吳, spoken in the Yangtse Delta and Shanghai (hence called Shanghaihua 上海話). Wu is the name of an old feudal state of the Spring and Autumn Period.
* Northern Min Minbeihua 閩北話, spoken in northern Fujian province
* Southern Min Minnanhua 閩南話, spoken in southern Fujian and Taiwan
* Hakka 客家, distributed in many provinces of South China and oversees. "Hakka" means "guest people"; the Hakka language "islands" are enclaves inmidst of territories where mainly Cantonese is spoken
* Gan 贛, spoken in Jiangxi
* Xiang 湘, spoken in Hunan
* Recently some dialects were classified as languages: Dongan (the language of the Muslim Chinese in the West), Jin in Shanxi, Mindong, Minzhong and Puxian in Fujian, and Huizhou in Anhui and Zhejiang.
Relatives of the Chinese Language are the Tibeto-Burmese languages, the languages of Tibet and of modern Myanmar and many, many small tribes that live in the Himalaya and its foothills. Thai and Vietnamese are definitely not related to Chinese, even if both are isolating (one word-one syllable) languages that have also tone pitches. English for example is also an isolating language, and many highly agglutinating (one word-one chain) languages like Turkish and Japanese have lots of one syllable nouns. Tone pitch languages exist all over the world, and tonality is no criterium for language relationship.
The vast country of China comprises many territories where people live that speak languages that are not related to Chinese, like Uighurs, Mongols, Tajiks, Koreans and Russians. And we don't have to forget the many national minorities in the southwest that speak languages related to Thai, Vietnamese and Tibetian. In Taiwan live a few aboriginal people of Malaio-Polynesian origin. The aboriginal people of southern China as well as the nomad immigrants in the north are long assimilated to the Chinese and are not distinguishible except a few officially accepted minorities.