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?

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?

If these questions have been answered a few hundred times, perhaps even in the FAQ I apologize and will hang my head in shame and go read those, if you'll just give me the link. I haven't seen anything about this, but perhaps I haven't looked hard enough.

I'll see if I can't come up with a few more scenarios later, if I can think of any.