We don't know of any bank in the U.S. that issues debit or credit cards that can be used for online gambling transactions. There may be some, and if anyone knows of any, please let us know via the QoD submission system and we'll post them as an update to this question.
Many people are under the erroneous belief that the reason the credit-card companies deny these transactions is because online gambling is illegal. This isn't the case (although note that some states do have laws that prohibit online gambling). It's actually primarily because of the amount of fraud perpetrated by the consumers (repeat: not the gambling sites, but the players). In too many instances, people charged and charged and ran up large gambling debts on their credit cards, then did chargebacks and claimed these charges were not theirs. So the banks tightened their policies.
A particularly notable event that triggered many of these policy changes involved one Cynthia Haines, a California woman who ran up $70,000 on her MasterCard account(s) while gambling on the Internet. She was sued by her credit issuer for the amount, whereupon she filed a countersuit saying that she shouldn't have to pay for those charges, her reason being that they shouldn’t have allowed her to gamble with credit in the first place. A 1993 California case, Metropolitan Creditors Service of Sacramento v. Sadri, had set a precedent stating that gambling debts are not collectible in that state. This eventually resulted in a settlement between the bank and Haines and led MasterCard to create much more stringent policies with regard to permitting such charges.
In addition to customer fraud, there has been pressure exerted on credit card companies, and American money transfer companies like PayPal, by government agencies. PayPal stopped allowing transactions with online gambling sites, and also paid a $10 million settlement with the government. In New York, Eliot Spitzer, acting as Attorney General, also put pressure on banks to disallow these transactions, and was able to get large banks such as Citibank to decline the transactions.
Over time, it appears that credit card companies just found it was more trouble than it was worth to allow these transactions.
The industry leader in money transfers these days is NeTeller (www.NeTeller.com ). You may register your bank account with them and then do electronic funds transfers back and forth. For people who have used PayPal, the system is similar. NeTeller was originally a Canadian company that began to thrive once PayPal stopped allowing online gambling transactions, becoming a huge and profitable business. It's now based on the Isle of Man and is publicly listed on the London AIM stock exchange. We feel comfortable endorsing NeTeller, not only as a safe third-party institution to give your banking information to, but also as your best avenue for online gambling.
Note: Sen. John Kyl (R-AZ) has consistently led the attack against Internet casinos. Over the past several years, he’s repeatedly introduced bills aimed at outlawing online gambling. (Interestingly, his stance — that online gambling needs to be made illegal — would seem logically to imply that it currently is not illegal, though he naturally downplays that suggestion.) This legislation is designed to attack the money-transfer systems that people use, including credit-card transactions and bank transfers. Since we're unaware of any credit-card companies that allow these transactions, and because companies like NeTeller are not based in the States, we're not sure that the bill would effectively do anything, were it ever to be passed. It would, however, make online gambling more clearly illegal, although whether this would have any impact on Americans gambling online is doubtful. In our opinion, it's the legislative equivalent of spitting in the ocean.