Today I learned! Yeah, hard to beat $5 a trade for US stocks.
....But not impossible!

You can also buy Schwab's ridiculously low cost index mutual funds via OptionsXpress Singapore. There is
zero trading cost to buy/sell them even via OptionsXpress Singapore, as I understand it. I'll list most of the interesting ones by symbol:
SWPPX, S&P 500 Index, 0.03% expense ratio
SWTSX, U.S. Total Stock Market Index, 0.03%
SWSSX, U.S. Small Cap Index, 0.05%
SWISX (International Stock Index) is also available (0.06%), but I think most non-U.S. persons should still choose the Irish domiciled equivalent, for tax reasons.
For example, if you buy SWTSX then the only costs you (a non-U.S. person in Singapore) will pay are the currency conversion charge (~0.3%) to get in, the world's lowest annual management fee (0.03%), U.S. dividend taxes (at 30% withholding), and whatever it costs to transfer funds back into Singapore (with the currency conversion), which depends to some extent on your choice of bank. That's not bad.
U.S. stocks, including these U.S. mutual funds, are (of course) subject to the U.S. estate tax.