Here's my understanding from reading [this reddit thread](https://www.reddit.com/r/taiwan/comments/2lu4u5/tap_water_in_taipei/) (how much more authoritative can you get?), looking at the [Taipei Water Department](http://english.water.gov.taipei/ct.asp?xItem=994056&CtNode=23900&mp=114012) website, and talking to an Airbnb host in the city:

**Tap water is safe in Taipei on the city's side, but most people boil or filter to be sure**, since old buildings may have dirty or faulty pipes.

I don't know about outside of Taipei.