Tourist visas to Taiwan have an associated "maximum stay" of 30 days. For those visas, how are the days counted? Does the stay begin on the partial day that the traveler arrives or the first full day spent in the country? Does it end on the last full day spent in the country, or the actual day the traveler departs?
Most ex-pats who are in Taiwan leave the day before visa expiration. There is a lot of back and forth within the government about what means what. While one bureau will give you one awnser another will tell you a different answer. This advice was actually repeated to me by an employee at the Ministry of Foreign Affairs. I have also had issues at immigration when leaving on the last day of my visa. I got through, but they had to interview me and I almost missed my flight out of Touyuan airport.
So, in general, we say leave the day before your visa expires. If you are on a 30-day visa, that is 30-days after your arrive, although it is technically valid to day 31.
The maximum stay for a 'visa-exempt' stay in Taiwan varies: it's either 30 days or 90 days, depending upon your nationality, so it is important to check which category you fall into.
In case of Taiwan, the duration of stay is counted from day after arrival. Here's the relevant excerpt from the Taiwanese Bureau of Consular Affairs:
End-of-stay in most countries is considered as the actual day a traveller leaves, so I assume it would be the same for Taiwan. There isn't much point in risking a half-day stay hoping the border control officers won't count it as overstaying.