Electronics
Laptop/charging cable
Bring necessary cords and possibly a back up power supply if you have a Dell. It would also be useful to bring a computer to AV/projector converter for Mac users since the cables don't plug in the same way here. Although Taiwan does not have a single Apple Store, there are unofficial Apple Stores from which to buy Mac products, though you may have to order something (i.e. charger) to be delivered to your store from Taipei, which can take a few days. For other computer needs, Taiwan is the perfect place to find any electronics. Note: fixing any Apple products in Taiwan is not cheap and immediate because there is no Apple store/Genius bar. There are many local stores that will fix products at a cheaper price at the risk of them not being official Apple stores. Fixing MacBooks here take a significantly longer time. If your computer ever gets wet, immediately stick it in an enclosed space with a dehumidifier for a day, otherwise your screen might start molding because you didn’t dry it out fast enough.
Adapters
The outlets in Taiwan are two-pronged, so if you have electronics that need three-prongs, you’ll need a converter/power strip. If you have electronics you need to use in the first week, make sure to bring a converter or buy one in the day-1 shopping trip. Also, it is advisable if you are bringing items like hair dryers to bring a voltage converter, or simply to purchase one when you arrive to be on the safe side. Items can short out dangerously.