Easy Card, also known as Yoyo Card in its Chinese pronunciation, is the most helpful item that you should have it with you during your stay in Taiwan.
You can purchase this card at any of the convenient stores in Taiwan, ( 7-11, Family Mart, OK, or HiLife ). The card itself costs you only 100NTD (about three US dollars), and you can charge some credits immediately after getting it in the store. Once it is charged, you can pay for your public system rides including metro in Taipei, buses in most cities, and local trains, or even for high speed railways if you have put enough credit in it. It is also very handy for cyclists to carry it since you will no longer carrying a lot of changes, and you can pay for your purchases in all convenient stores mentioned earlier and also major supermarkets where you usually get your supplies on the way traveling in Taiwan.
The only thing that you have to pay attention is that this card is not registered with particular name, so once it is lost, whoever picked it up can go ahead and use all the credits inside the card and there is no way to trace to it. Therefore, be careful of how much to charge at one time and take good care of it while carrying it.
BTW, worth to mention is that if you use Yoyo Card while utilizing the public transportation systems, you often get a certain level of discount. For example, in Taipei MRT, there is a 20% discount for using Yoyo Card instead of single journey ticket. And in Taichung, if you use Yoyo Card to pay for the bus fare, you could enjoy the first 10km for free at each trip of bus ride. Also, having a Yoyo Card and registered it with the youbike system, you will be able to enjoy the following cities in the best pace, bicycle riding, and some even give you first 30 minutes bike rent for free. Cities that have the youbike systems are Taipei City, New Taipei City, Tayuan City, Taichung City, Changhwa County, and Hsinchu City.
The benefits of having an Easy Card with you continue more and more, and hope your trip in Taiwan have more and more fun.