some of these replies actually hurt my eyes... In order to avoid confusion:
- the blockchain = the technology behind bitcoin, recording all transactions in a public ledger
- blochchain.info = a website that offers services based on the blockchain
While the first is merely a piece of technology, the second is a company. The company can possibly do some data mining if they really wanted to.
- when you buy bitcoins, usually your name, address, paypal account, credit card, id,... or other forms of identifying information are needed. If somebody (FBI, interpol,...) wanted, they could easily find out who bought coins and on which address they were stored.
- when you trade your bitcoins for fiat or for physical services, the same information is needed, and the feds can link your identity to your wallet address.
- if somebody is really dedicated, he can follow the trail of the coins, unless you know how to conceil the coin movements (by using mixing services, coinjoin, exchanges,....)
This means that it doesn't matter if you use a VPN, tor or the computer in your public library, if you don't know what you're doing, somebody can follow the full trail of the bitcoins, from the moment they were mined, to the moment you bought them, to the exact moment where you traded them for dope, to the moment the dopedealer sold them again for fiat.
Luckily, if you're not doing horribly illegal stuff, i'm pretty sure law enforcement has better things to do than to find out who gambled $100 on dice or if you bought $50 worth of weed... I could be mistaking tough