Cash has already been ruled out, properly so. Banks don't want to deal with the stuff in any large quantity, and they charge to handle it. There are declarations to make as it's carried, and there is significant risk of loss, theft, or confiscation. Not recommended.
Interactive Brokers has a local custodial account in Singapore at Citibank. Assuming you have opened a Singapore dollar-denominated (SGD "base currency") account with IB, you use GIRO or FAST to transfer funds into their custodial account. Total cost so far: zero. Usually within an hour or two of receipt the funds pop up in your IB account. You then go to the Forex section of their trading site and buy U.S. dollars. You can set a limit price and wait, or you can execute the trade immediately at a
very narrow spread. IB charges 0.2(*) basis points (0.002%) for the conversion with a minimum of US$2 per trade and US$10 in commissions per month (assuming a minimum US$2,000 account balance value; US$20 otherwise). For "mere mortals" the minimum commission will govern, and it will for a $100,000 sum. Total cost so far: IB's commission plus the (very narrow) spread, arguably less if you're slightly patient and set a limit price. Finally, you withdraw the U.S. dollar funds via the ACH (U.S. domestic clearing) network to your U.S. bank or credit union. (Both the sending and receiving bank accounts must be in your name.) You can make one ACH withdrawal per month free of charge.
That's pretty tough to beat, at least for "thousands and up." If you're trying to convert $100 then yes, try Raffles Arcade. If anybody can beat IB, please let me know. I'm always interested in alternatives.
....One alternative that generally doesn't beat IB is Charles Schwab, but it's worth mentioning since Schwab can still be a good option. If you have a Charles Schwab brokerage account in the U.S. (free to have) then you can deposit Singapore dollar funds into Schwab's custodial account in Singapore via GIRO or FAST. You can't control the exact timing of the conversion -- no limit price available -- but that path seems to result in a pretty good total cost of about 0.3%, plus or minus. There's no charge for the GIRO/FAST transfer inbound, and your funds automatically land in your U.S. Schwab account, ready to do whatever you want (including free ACH transfer out if you wish). So if you're in the "hundreds to thousands" monthly range I think I'd recommend Schwab for the Singapore-to-U.S. remittance path. Charles Schwab (even the brokerage; you don't need a Schwab Bank account) has a fantastic debit/ATM card as well that's great for international travelers: no foreign exchange fee (except for whatever the Visa network charges) plus ATM fee rebates if the ATM operator charges a fee. That might be the best debit/ATM card in the world right now.
....For what it's worth, my current favorite U.S. credit card is the obscure Citizens Bank CashBack Plus World MasterCard -- assuming that you set it up for automatic full monthly balance payment, as always with credit cards. And assuming you don't use the card at an ATM and only use it for merchant purchases. That card gives you the pure MasterCard network rate (slightly better than Visa's) with no foreign exchange markup plus a 1.65% rebate, assuming you use the card at least once per month. (If you don't then you get 1.5% back -- still excellent.) The only thing I don't like about that card is you've got to call them up (on the phone) to let them know about upcoming use of the card outside the United States. You can't notify them online yet, unfortunately. There's no annual fee for that card.
(*) Less if you're converting US$1 million or more. Most of us are not, sadly.
