If you want to pay for something anonymously on the internet, you can use a prepaid gift card. It will generally be accepted just like a credit card (though there do seem to be exceptions). It doesn't require registering your address or SSN. Or at least not in the case of Vanilla Visa (they require, IIRC, a name and zip code, but there's nothing preventing you from faking those). You can't refill it, so you'll have to keep paying for new ones if you intend to do it a lot, but I guess that's the price.
You got lucky. Most sites won't let prepaid gift cards go through. For example, neither Amazon nor PayPal, IIRC. Vanilla Visa was exactly the one I had, that ran into the problem, and I'd even put in my name and ZIP on their web site.
The problem seemed to be the lack of a billing address -- what are you supposed to put? Nothing worked. On another site that processed their credit cards via PayPal, it didn't work either. I called PayPal customer service and they explicitly told me they don't support cards that don't provide a means to verify a valid billing address and 3-digit security code.
Every time I get a VISA prepaid gift card, I simply buy an amazon gift card with it. I've never had any problems doing this.
Now, it's not like I don't have other identifiable information on my amazon account (a real credit card, a previously used shipping address, etc), so it's not anonymous, but they do accept prepaid cards.
Hm. I just used an arbitrary address consistent with the zip code. But I must admit that though it's worked in most of the cases I've tried, I have no idea what fraction of online merchants take such things in general.
Bitcoin transactions are all public. If you want to be safe, you have to use a laundry service, and I don't know how good those are.
Here is a thought though: what if you got a prepaid credit card in another country? I suspect somewhere in Europe would be your best bet.
Also, how would the card company know that the transaction was online? It would be shady as all hell, but couldn't the merchant open a cornerstore and ring up all the online orders as chips and a smoothly?
I'm not an expert, but I think credit card companies themselves may be pretty unhappy with something like that. It's a tricky proposition in the first place, accepting CCs as an online (or even brick & mortar) merchant. You are effectively assuming some funky risk. Fraudulent transactions mostly your problem, at least more yours than the credit card company's, the bank's, the credit card owner's or even the fraudster's (in practical terms).
I wouldn't be surprised if by breaking or even nudging their rules comes with a high enough price to kill the whole thing. You would be open to being ripped off painfully and your merchant account would probably be shut down pretty fast.
What you've described is essentially how credit card processing for online gambling works. Except it's shoe stores and other places that sell stuff similarly priced to what an online gambler might charge his card.
Prepaid American Express is pretty easy, you can call and give them an address, they don't ask for a SSN (many legitimate people won't have one). Just say that you're making an online purchase and need an address for verification.
Not true, you'll likely have to go through a bunch of prepaid providers but there are certainly providers where all you have to provide is your postal code.
I run pretty much everything through these cards online to avoid fraud / identity theft issues and prefer the ones that are easiest to register for online purchases.
Bitcoin transfers are anonymous but not untraceable, eg. with enough circumstantial evidence surrounding the transfer you can be fairly certain who made it... if you use a wallet service then its not really anonymous at all if you have access to the wallet providers database.