The definitive answer is that there is no definitive answer. However, there is no federal law specifically outlawing online gambling.

The feds are trying to say that the Wire Act, which is the law bookies are prosecuted under, applies to internet gambling. The courts so far have not agreed. State law CAN prohibit online gambling, and some like Nevada do, although those laws are rarely enforced (as you've seen in photos of people playing at Party on a laptop while sitting at a table at a casino in Las Vegas).

As you saw on 60 Minutes, what anti-gambling politicians want to do is to go after the credit card companies and banks, so that you can't transfer money in or out. They tried prosecuting them under the Wire Act and it has so far failed. So now they're trying to pass a new law to prohibit transfer from a credit card or bank account to a gambling site.

The problem there is that there's already a middle-man: Neteller, FirePay, and others. They are not gambling organizations, so transfer from your bank to them would probably remain completely legal (while the politicians would claim a victory because their law would "make it harder" to wager online).

So, by and large, I don't think the average American citizen has much to worry about.