Thanks for some very interesting answers. I'm trying to write some followup questions to some of the topics that have been brought up.
I have put together some scenarios, or use-cases. I'd love some thoughts about these too.
1) I am a conservative senator with very traditional values, focus on the family and such. I do however in my spare time purchase gay porn. Naturally I don't want to associate my visa-card with such activities, so I buy some bitcoins with said card and then spend those in a shop which caters my interest. I do this though TOR or some other anonymous service, perhaps a VPN bought with bitcoins. How long, if ever, does it take for the journalists to show up at my door?
It really depends upon, not just how careful you are, but how careful the gay porn site is. This is why bitcoin is psudoanonymous, not truly anonymous. You can actually choose to not disclose your identity to the porn site, but you really cannot
hide it from a determined investigator. If a reporter were to associate one or more bitcoin addresses to the gay porn site, and then associate one of the addresses that have sent them money with you; then use of Tor doesn't matter, you're going to be on the news.
2) I am a computer professional who decide to run a service in I2P that is somewhat "gray" in the legal sense. A service that has both legal and illegal uses. I allow people who wish do donate bitcoins to this service. I already have a bitcoin wallet which I use for things that are 100% legit, so I use a receieve adress which is only used in the I2P-service. Will my anonymity be compromised by recieving bitcoins? Will it be compromised when I spend coins on the "open" internet?
Again, this isn't about the security of Bitcoin itself. If the bitcoin address(es) used to receive donations for said service are associated to yourself, you're burnt. And yes, you could out yourself by sending the coins to another address of your's that is known to be yours, or by spending those coins with someone or some site that could be compelled to tell the interested who it was that bought something with those coins. There may not be a shipping address, but there would be other clues in the logs that a talented investigator could use.