I've used both Sam's Club AT&T and MCI prepaid cards in all 3 places. They have both worked well. Yes, I know that there are cheaper solutions. But these have always worked, too.

The Costco MCI card gets worse rates than the Meijers MCI cards that I bought 1-2 years ago (on sale).

Note that for Japan, you will need to print out ALL of the access numbers and match the correct number to the brand of phone that you are using, especially from coin phones. example: Use the NTT AT&T access number when using a NTT coin phone. Once I found a combination that worked, I just used that brand for the rest of my trips. These are usually green or silver, depending on the brand.

Also, some of the listed countries (certainly Japan) will require a coin drop for a dial tone. But the coin will be returned. Using the AT&T access number from the Singapore Conrad I was charged about 1 USD for the local connection from my hotel room.

Another option is buying prepaid SIMs for Hong Kong and Singapore and using them in your unlocked 900-800MHz GSM cell phone. This won't work for Japan due to their unusual cell phone systems and their 2100 MHz. service.