In order to placate the Government of the People's Republic of China, most countries have only friendly, unofficial, de-facto relations with the Taiwan-based Republic of China. This means that most countries only maintain an "institute", "commercial office", "friendship association", "economic and trade office" and so on in Taiwan, which all function as de-facto embassies. Most of these representative offices provide full consular services as any other embassy or consulate in the world, meaning that one should contact these offices if one gets in trouble in Taiwan. Nevertheless, these representative offices have no diplomatic status and enjoy no extraterritoriality.
On a side note, the former US ambassador's residence as well as the former British Consulate have become tourist attractions in Taipei. See Attractions.
List of Embassies or Missions
The Ministry of Foreign Affairs of the Republic of China provides a list of embassies or missions in Taiwan. If you need to contact with the embassy or mission of your country, please call by phone or visit the mission's website first to confirm the address.