The real danger of Taiwan is the traffic. Again and again I hear foreigners get caught up in the insanity people call road traffic here. Shortly ago the founder of a stray-dog rescue organization in Taiwan reported he saw an English teacher (from Canada if I remember correctly) being injured fatally by a truck changing lanes; the dog rescuer managed to comfort the dying man a bit. Recently there was another fatality of a foreigner mentioned. And in October a teacher of the Taipei American School was fatally injured when crossing the road (http://www.tas.edu.tw/page.cfm?p=464&newsid=99). There is hardly any crime on Taiwan's street, but the real danger lies with untrained drivers having a lot of unjustified self-confidence when driving. They hardly use the mirrors, step on the gas as if engaged in a race and are often under the influence of alcohol or somewhat stimulating soft drugs like betlenut taken in combination with stimulating or sense-deafening local "energy" drinks like "Whisby" (originally created to replace alcoholic drinks).
Taiwan is a safe and very guest-friendly country and a great place to be introduced into a friendly version of Chinese culture. But please be damned careful on the roads. Or when stepping out of your apartment door.