There are a very few situations where no visa is required or you can obtain a visa on arrival.  The following paragraphs explain the main exemptions.  You should also be familiar with airline regulations.

 1. Visa Exemption for Diplomatic, Service or Official Passport Holders
China has mutual visa-free agreements with some foreign countries, but they are mainly for diplomatic, service or official passport holders and only allow the duration of stay less than 30 days.

 2. Visa Exemption for Direct Transit
The truly transit passengers by international flight who hold onward tickets do not require a visa  provided that they stay in the airport transit area and depart within 24 hours.

Citizens of the following 30 countries are permitted to transit Shanghai for up to 48 hours without a visa (They are allowed to leave the Pudong Airport/Hongqiao Airport to enter the city): Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, New Zealand, Norway, Poland, Portugal, Republic of Korea, Slovakia, Slovenia, Spain, Sweden, Switzerland and USA.

 3. Visa Exemption for Nationals of Singapore, Brunei and Japan
Ordinary passport holders of Singapore, Brunei and Japan are allowed to enter China without visas for up to 15 days for tourism, including visiting family or friends, or minor business purposes provided they enter through nominated international ports.

For nationals of these three countries, a visa is required under following circumstance: 
(1) Ordinary passport holder visits China for tourism, business, visiting friends and relatives and stay for more than 15 days. 
(2) Ordinary passport holder visits China for the purposes of study, work, official visit, settling down and interview.
(3) Diplomatic and Official passport holder.

 4. Visa Exemption for Holder of Aliens' Residence Card
Foreign nationals who visit China for the purposes of study or work and resident foreign journalists shall apply for Aliens' Residence Cards at local public security authorities within 30 days of entry into China.

Within the period of the validity of the Residence Card, the holder is entitled to enter and exit China for many times without applying for another visa.

 5. Visa Exemption for Holder of  APEC Business Travel Card
The APEC Business Travel Card is regarded as a multiple entry visa valid for three years. With this card and relevant passport, the holder is entitled to enter China for many times within three years. The duration of each stay should be within 2 months.

 6. Visa Exemption for Visiting Hainan Province
Citizens holding the ordinary passport of the following 26 countries are exempt from visa requirements when they travel to Hainan Province as a group (at least 5 members) organised by International Travel Agencies that have been set up and registered in Hainan Province.  The stay is limited to 21 days and travelers are not allowed to leave Hainan: Australia, Austria, Canada, Denmark, France, Finland, Germany, Great Britain, Indonesia, Italy, Japan, Kazakstan, Republic of Korea, Malaysia, Netherlands, New Zealand, Norway, Philippines, Russia, Spain, Sweden, Switzerland, Singapore, Thailand, USA and Ukraine. The tours organized by travel agencies of South Korea, Germany and Russia can have two members each group.

 7. Visa Exemption for Visiting the Pearl River Delta Region
Citizens holding passports issued by the nations with diplomatic relations with China is exempted from applying for a visa if he or she joins tourist group at Hong Kong and Macao organized by registered travel agencies in Hong Kong and Macao to visit the Pearl River Delta region (Guangzhou, Shenzhen, Zhuhai, Foshan, Dongguan, Zhongshan, Zhaoqing, Huzhou Municipalities) for tourism and stay up to 6 days.

 China Visa Application Requirements
Requirements for China Visa Application at China Embassy/Consulates in USA
Requirements for China Visa Application at China Embassy/Consulates in UK
Requirements for China Visa Application at China Embassy/Consulates in Canada
Requirements for China Visa Application at China Embassy/Consulates in Australia