Taipei’s subway system (the MRT) opened in 1996, with construction taking place between 1988 and 2009. The system is cheap, clean, easy to navigate, and extraordinarily accessible.
Here is a trip through the system, from an accessibility point of view:
As you approach the station, which may have several numbered entrances, look for a sign indicating an entrance that is accessible (the elevator symbol with a wheelchair next to the large entrance number):
Now look for a sign directing you to the accessible elevator:
Here is the ramp leading to the elevator:
Inside the elevator, you will find lowered controls, and signage in Mandarin, English, and Braille:
Also in the elevator, and on the trains, you may see information about any elevator outages in the system, with information about what your alternatives are:
Having purchased your EasyCard or one use ticket, look for the wide turnstile:
Once inside the turnstile, you will find signage for accessible routes to the platforms, and for accessible restrooms:
Once on the platform, you may enter any car, but the cars at the beginning and end of the train have extra space for wheelchairs. If you may need assistance, go to the front of the train as indicated by the wheelchair loading zone sign, where station personnel or the train conductor will help:
The train doors are wide, and the gap between the train and the platform and the train is level and minimal. On the platforms and in the trains are constant reminders to yield to disabled passengers:
On the trains, I’ve seen courteous yielding of priority seats to the elderly, the disabled, pregnant women, and people with children.
Once at your destination, look for signage indicating which exits are accessible:
and for signs indicating the direction and distance to the elevator:

Wow.
Just wow.
Yay!
And I forgot to mention in the post that every time I’ve been on the MRT so far, I’ve seen independent wheelchair users (and many wheelchair users with assistants).