Just now (2006 Nov) I have managed to make BofA’s ShopSafe thing work for me. It seems to be a newly acquired unit of Bank of America. (I think it was once MBNA Corp.) BofA’s pages link directly to it. In a few clicks one gets a “Temporary Authorization” which seems to be in effect a separate credit card with its own 16 digit card number plus a three digit security code. It also has an expiration date. I already had a BofA Visa card so it was especially easy for me. I got some background here.

I:

The rest is fairly obvious and quick. To use your new ‘card’ to pay someone you will need: These can be retrieved later thus:
> Activity > View Active ... > click on some line > Use Number

Use the ‘Activity’ tab to see what Temporary Authorizations are in effect and their status. You can delete them or extend their limit. I didn't need to agree to any new terms.

I used this new number to pay SecondLife. I discovered that I had to enter my name there with normal capitalization instead of how it appears on the card in all caps. SecondLife took their money which I verified soon thereafter at the BofA site. My SecondLife stipend showed up promptly. So-far, so-good. I will report problems here.
(2007 Apr) As of now I have used this service several times with no problems.
(2007 October) I stumbled on the (reasonable) restriction that one such CC number can be used with only one merchant. It says this in the FAQ. Perhaps you should read the short FAQ. I didn’t.

I think there are other services like this. Other rumored names are