Taiwan (臺灣 Táiwān) is the common name of the Republic of China (ROC) which governs the island of Formosa and several smaller outlying island groups of Penghu, Kinmen, Matsu, Lanyu (Orchid Island), and Green Island.
There is a page on Taiwan Rules.
globulon?- There seems to be some understandable confusion on these topics. I am a foreigner who has lived in Taipei for 3.5 years at this point, but I am married to a Taiwanese. I'm not a linguist or anything.
On the language question: Everything public is Mandarin. In schools everybody studies Mandarin. If you speak Mandarin you will have no problems getting around and interacting with people in most places you are likely to end up. (One slight source of confusion may come in if you speak just a bit of Mandarin because there are actually a lot of different ways of saying Chinese and China in Mandarin that don't refer to different dialects etc but just have different flavor or emphasis on who they are including or excluding etc).
There is a dialect which in English we call Taiwanese (this is a bit confusing because you would expect this to be the official language of Taiwan but it's not.) As has been pointed out below, this dialect originates from the Fujian province of the mainland. In Mandarin here in Taiwan it is referred to as Tai-Yu. The Hokkien name mentioned below is right for the family of regional dialects that Taiwanese is from ( https://en.wikipedia.org/wiki/Hokkien)but that's not how Taiwanese people refer to the dialect that is spoken in Taiwan. I believe they are still pretty close but consult a linguist if it is important to you to get the details ironed out. This is way far and away the most common dialect after Mandarin throughout the island. It is possible but unlikely that you would meet people who speak only Taiwanese and don't really speak Mandarin. This is more probable the more south and the more rural you get. On the other hand, in Taipei in particular there are plenty of people who speak Mandarin and do not speak Taiwanese.
It is true that the characters are traditional which means that they are more complex. For this reason it is likely to be easier to read the simplified if you already know the traditional rather than the other way around.
There are a good number of other dialects on the island, but it is quite unlikely that if you are just visiting the island that you would have anything to do with those dialects, let alone get into a situation where it was the only language option. (If you want to know there are actually a lot of Japanese speakers particularly in the older generation from the time of the occupation.)
Just for reference, in Taipei it is easy to get around without knowing any Mandarin or Traditional characters as many signs are in English and many people have some degree of English. Obviously it will limit what you can do but you can still have a great time.
The organization and club scene is also a bit complex. I am trying to collect relevant info here ( http://www.lifein19x19.com/forum/viewtopic.php?f=10&t=12076&p=190951#p190951)
Malweth - I'm heading to the Taipei region (Chung-li) late summer this year and wondered what kinds of Go resources I might be expected to find? Just wish I spoke Mandarin...
gimpf: Don't worry about Mandarin, although taiwanese people can speak it, they have their own, quite different dialect too :) And, if this wouldn't be enough, enjoy the traditional chinese characters instead of those we learn in our language courses...
user : There are precious few go clubs. The one which was closest to me recently closed down. What you are looking for now are the Children's Go Schools. There is one in Kaohsiung. There is one in Tainan. is also a Goban factory in Taoyuan. You can use Yahoo Babelfish or Google Translate to look at the page. They might have someone there who speaks English depending on the day. http://goodgo.com.tw.
unkx80: The Taiwanese often speak in a Chinese dialect known as Hokkien, just as the Hong Kong people often speak in another Chinese dialect called Cantonese. While it is true that the Chinese did unify the written language, they did not unify the spoken language.
malweth: As I understand it, Hoklo are the native people of Taiwan, and their language is not a dialect of Chinese (though it may have some influences from Chinese). The Chinese have unified the written language, except for Taiwan which uses the "Traditional" characters (rather than the "simplified"). Additionally, however, the Chinese language was unified, or at least made official. Pu-tong-hua (Mandarin) is the official language of China (called Guoyu in Taiwan), though Cantonese and others are still used. This is all quite off topic, however... :D
ajility?: There is a bit of confusion here at the moment. The Taiwanese dialect is called "Hokkienese" meaning Fujianese, the dialect spoken by Han Chinese in the mainland province of Fujian which is opposite Taiwan. The term Hokkien is also used to describe the Hoklo indigenous peoples of Taiwan, who naturally speak a non-Chinese language. The two groups are sometimes called the same name because they both lived in the same place (e.g. way the heck far away from any of the historical capitals of China). Nevertheless, there is a Fujianese-like Taiwanese dialect spoken commonly in Taiwan, especially outside of academic/business settings or by those without much education.
Alex Wang: Does anyone know of any go salons on the island? If so please tell me, thanks.