A good moving company if you speak no Chinese. Most of the people at Allied Pickfords speak enough English to help you with your move. The prices are average and they are reliable with times and being carful with your belongings.
Crown Van Lines is another international mover company, but they can also deal with local moving. Their English service is usually pretty good on the phone, but it's a good idea to have your address written in Chinese to show the actual movers. You can also check out their website at www.crownvan.com.
ASG Four Winds is a Taiwan based moving company. They can both move and pack your items. The telephone operators speak English and are very helpful. The minimum charge per truck is 15,000nt.
Green Van International can move both locally and internationally. They speak English and are helpful over the phone. They charge minimum 8,000nt per truck.
United is very English speaker friendly. They offer services other than moving, such as warehouse storage and they can move your pet. For local moves the minimum charge is 7,500nt.