What to do with a 4 hour lay-over at Taipei International Airport (Taiwan)?

The Novotel Airport hotel has a spa and there is an airport shuttle that you can use. Its very close to the airport. The Evergreen Transit Hotel might have an exercise room and its in the airport complex. You can also shop, eat, check out the museum displays, art exhbit, and there is also a business center called "The More" there.

Play wii, use internet, eat some taiwanese food.

Taipei International Airport is rather dull compare to Singapore Changi Airport,therefore you can do nothing but to sleep to kill time. I suggest that you should extend your visit even just for 1 day if possible,cuz you don't want to miss out the beauty of Taiwan.

check out this website: http://www.taiwanhotel.com.tw :)
where you can find very useful information.

Find a girl.
You can get lots of "exercise" in 4 hours.
Other than that there isn't much to do at the airport.
Taoyuan is the closest big city but it takes a while to get here.

4 hours really isn't enough time to do much. The airport itself is rather sterile and boring - they don't even provide free wi-fi. There isn't anything close enough that's worth seeing. I suppose the suggestion already provided of the hotel spa is the best you could do - although it will be plenty pricey.