For people who would normally require to obtain a visa in advance there are certain emergency situations which will permit them to get a visa on arrival.  These will always require an invitation from an accredited Chinese organisation which explains the emergency, (mostly related to business purposes which from the Chinese perspective it is important that you are admitted without delay) or you must yourself be in a real emergency situation such as a passenger in a plane or ship in mechanical difficulty.

Aliens who hold ordinary passports issued by countries which have diplomatic relations or official trade links with China as well as letter(s) or telegram(s) from authorized units in China, may, under any of the following circumstances where they must necessarily rush to China but have no time to apply for a visa, may apply to the visa-granting departments at entry ports as authorized by the Ministry of Public Security. The Rules on Visa Issued at Entry Ports are not applicable to the nationals of United States.

1. They are invited at the last moment by a Chinese host to come to China for a trade fair.
2. They are invited to come to China to submit a tender or to sign a formal economic or trade contract.
3. They come to China by appointment to supervise the inspection of import and export commodities or to participate in a check-and-accept operation in accordance with contracts.
4. They are invited to participate in the installation of equipment or in the emergency repair of engineering projects.
5. They come to China at the request of the Chinese side to solve a problem of claims.
6. They are invited to come to provide technical advisory services.
7. They come to China due to a last-minute change in the composition of a visiting group and with consent of the Chinese side after the visas are granted.
8. They come to China to see patients in critical conditions, or to undertake funeral matters.
9. Owing to force majeure, transit visa holders cannot leave the country within twenty-four hours by taking the original place or by taking other means of transport.
10. Other invited guests who really have no time for visa application to the aforesaid China's resident agencies abroad, and who hold letter(s) or telegram(s) from competent authorities who give the consent for the invited guests to apply for the visa at the designated entry ports.

The visa-granting agencies at entry ports shall not accept and handle visa applications filled out by people who do not come under the aforesaid circumstances.

Some accredited International Travel Agencies incorporated under Chinese laws may apply for group-tour visa at entry ports with Visa Notification Form issued by provincial office of foreign affairs.

Visa-issuing departments at port of entry, as authorized by the Ministry of Public Security, are stationed at the following ports: Beijing, Shanghai, Tianjin, Chongqing, Dalian, Fuzhou, Xiamen, Xi'an, Guilin, Hangzhou, Kunming, Guangzhou (Baiyun Airport), Shenzhen (Luohu, Shekou), Zhuhai (Gongbei), Haikou, Sanya, Jinan, Qingdao, Yantai, Weihai, Chengdu, Nanjing, Changchun, Huichun, Hekou, Mohan.

There is also provision for a short stay (5 day) 'visa on arrival' for some nationalities for persons who only want to visit a Special Economic Zone such as Zhuhai or Shenzhen.  Most travellers would find this not an option if they intend flying there.  See Airline Regulations