I guess in the strictest sense it is true you can get everything here in Singapore, but lots of it will be made different, pricey and in short supply. I would bring:
High Quality Sheets and Towels (beds are a different size here than Europe, UK, Australia, NZ and US)
Lots of DVDs (now downloading certain shows from certain sites is a problem)
Books
Favorite OTC Pharmaceuticals
Jeans
Shorts
T-shirts
Bras & underwear, for sure
Shoes, shoes and more shoes (lots of running shoes here, but if you are a bigger size -- stock up at home)
There's more, just give me time...