Pe̍h-ōe-jī (POJ) is the most widespread system of romanized Taiwanese. Introduced by Western missionaries around the 1860s, the long association it has with the Presbyterian Church in Taiwan (and previously in Fujian too) explains why it is also sometimes called the Church Romanization, although proponents of the system often discourage this name, in an effort to try and establish POJ as a secular standard.
Taiwanese for 'vernacular writing', Peh-oe-ji is the only romanization to be able to claim a significant number of readers at one time, although nowadays only a small number of enthusiasts and elderly Christians remain as users of the system. POJ is the only romanization which boasts a sizeable amount of literature, both secular and religious, plus a version of Wikipedia in the orthography. It is also the standard romanization used throughout this site.
See the comprehensive Wikipedia article for more information.