I agree with what Candice said about zhuyin. Besides, pinyin just makes no sense for Taiwanese. It is very hard for a Taiwanese to learn to spell characters with pinyin (my friend had tried. She never succeed.)
As for the "simplified characters" question, each Chinese character is based on certain making rules, which we call 六書. And Chinese government adopted simplified characters because this way, people would be able to learn reading and writing more easily at a time when the literacy rate was still quite low. But traditional Chinese literature are all written in Traditional characters. Therefore it sometimes causes problems if one who learned Simplified Characters first wants to study traditional Chinese literature later.
Although Simplified Characters are easier to learn, they can't present the beauty of many Chinese literature properly (as well as calligraphy, for example). That's why we are used to Traditional Characters.
However, some youngsters do tend to use some Simplified Characters nowadays, such as 体 for 體, 囯 for國 . ( this trend is deemed inappropriate by the elders.)