Almost every computer and high end electronic device in the world has something made by Foxconn.
My favourite is Franz. I love the products so much that I act like its official sales person. (They really should pay me, considering all the business I get for them) I love what the company has achieved in pottery making, it puts the bullet train approach to shame. I have its jewelry, its teapots, vases. If you have to get one Taiwanese souvenir, then this should be it. They have land in Jingdezhen, on the mainland and this company actively did so much for the region that even the Chinese Govt. thanks it and has shown its appreciation of the same. The company is really eco-conscious, at the helm of cutting edge technology and through R&D has brought down the temperature of the kilns, thereby saving on power, and cutting pollution and all that. (Do I sound like a sales rep.?) Then again, it is the products that wow me!
EDIT: I had seen their furniture line (prototypes only) but they were not selling it at the time, they are selling it now http://www.jeanboggioforfranz.com/ and frankly it is a bit kitschy. The whole furniture line has a boudoir thing going about it, chiefly coz it was designed for fashion houses in France. Good for a dekko but unbuyable (and unaffordable).
85C - better than Strarbucks.
Seconded. Times about a million. Twice as good at half the price! And their coffee-flavoured nougat is to die for! 
Love Family Mart, too. And the usual electronics companies and food companies. And books.com.tw. And Rhino for outdoorsy stuff and Merida and Giant for bikey stuff at fair prices. Oh, and the nougat at Sugar and Spice. And THSR. Okay, I’m done. For now.
aNueNue - High quality ukuleles from Taiwan)))
Punky Hair Products. Specifically because of their keratin hair repair mask. Its Awwwweeeeeesoooommmeee (in high operatic voice)
Dorcus Bikes
They copied a very expensive corratec carbon frame quite good, so I decided to buy this one and saved the half of the corratec frame.