As I also moved here last year from the U.S., let me add to the terrific list that preceeds this one.
Bring a grill! Or two! Share with your friends and neighbors! Grills are VERY expensive here.
I have found that wire coat hangers tend to rust (especially in the container on the way over), but I second the motion to bring plastic or wooden hangers. Wooden ones are available at IKEA, but the plastic ones here are much inferior to the ones from WalMart.
Do bring your videos, but music is cheaper here. Go figure! If anyone in your family is a gamer (playstation, nintendo, etc.), the selection of games here is limited and expensive.
Bring lots of clothes! The quality and fit of clothes here is not the same. The few items that are comparable are outrageously priced. Undergarments for men, women and children are not available in the brands and styles that we are used to. Bring chic clothes for a tropical island, but remember that many places overcompensate with the air conditioning so there are times that you will need sweaters, pants or light jackets indoors.
Shoes - Asian shoes are much wider and smaller than American shoes. I wear a ladies size 6 in the U.S. so I assumed that I could find shoes here. Wrong! I can find the length, but the shoes are so wide that I can't wear them. Men's shoes in large sizes are very hard to find and the selection is quite limited. Rubber soled shoes for men are a great idea - even dress shoes. When it rains here (almost every day), the marble floors are incredibly slick. Falling down outside your office is not a good look. Waterproof is a good idea, also. If you travel much in Asia, you may find that when it rains you will be standing in sewage. Never a problem in Singapore, but who wants wet socks, anyway. Think tropical rain storms.
Wooden furniture and decor items are terrific here, but beds, sheets and towels are not the same sizes as in the U.S. Recliners must be made of gold considering the cost.
Plan on buying carpets here. Selection, quality and prices are so much better than the U.S.
No matter what you bring, you will have a list a mile long the first time you make it back to a Target or WalMart. And even people who hated American malls before coming here miss them. It is a great life, but it is not like the U.S.!
Don't forget your Advil! Can't buy that here without a prescription.