I wonder if Swedish citizens are required to apply for a tourist visa before visiting China or if we have visa-free entry like in many other countries, or visa on arrival?
According to the Consulate-General of the People's Republic of China in Gothenburg:
Foreigners to visit China are generally required to apply for visas in advance. But ordinary passport holders from Singapore, Brunei and Japan can gain access to China without applying for visas for up to 15 days for business, sightseeing, visiting relatives and friends, or transit. They can enter and exit from the ports that are open to foreigners.
Swedish citizens are not in the list of citizens who have visa-free access to China. So you would need a visa to visit mainland China.
But, according to the Embassy of the People's Republic of China in the Republic of Estonia, Swedish citizens can be granted visa-free stays while transiting via China. This can be done by getting a connection to a third country.
1. 24-Hour Direct Transit
Under the 24-hour visa-free transit rule, no visa is required for international flight, ship, or train passengers who transit directly through mainland China and will stay for less than 24 hours. Passengers should hold tickets to a third country or region and have a confirmed seat.
Those who transfer in more than one city of China within 24 hours can also enjoy this policy. For instance, if one's trip is Moscow – Lanzhou – Guangzhou – Bangkok and the total time in China is less than 24 hours, the passenger can still enjoy the 24-hour direct transit. But the passenger needs to apply for the temporary entry permit upon his arrival.
2. 72-hour Visa-Free Transit
Passport holders of the following 51 countries and regions can be granted a visa-free stay up to 72 hours while transiting via Beijing Capital Airport, Shanghai Pudong Airport, Shanghai Hongqiao Airport, and airports of Guangzhou, Chengdu, Chongqing, Shenyang, Dalian, Harbin, Xian, Guilin, Kunming, Hangzhou, Wuhan, Tianjin, Qingdao, Nanjing, Changsha, and Xiamen:
24 Schengen Agreement Countries: Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland
144-Hour Visa-Free Transit
Passengers from the above countries transiting in Nanjing Lukou Airport of Jiangsu, Hangzhou Xiaoshan Airport of Zhejiang, and all air, sea and railway ports of Shanghai, including Pudong Airport, Hongqiao Airport, Shanghai Port International Cruise Terminal, Wusong Passenger Transport Center and all railway stations in Shanghai can enjoy a visa-free stay up to 144 hours in Shanghai, Jiangsu, Zhejiang. Passengers can enter and leave from any of the above ports.
Also, according to the Consulate-General of the People's Republic of China in Gothenburg, you can visit Hong Kong without a visa:
Ordinary passport holders from Sweden can gain access to Hong Kong without applying for visas for up to 90 days for business, sightseeing, visiting relatives and friends, or transit.
I recommend you read this Wikipedia article if you want to know which countries you can visit visa-free. It is generally a good source of information. However, make sure you also check with an official source before actually traveling to a country, to make sure you can really travel there visa-free. Official sources include: embassies, consulates, updated government websites (preferably official websites that belong to the country you are traveling to), etc.