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I'm sure somebody somewhere would/will be happy to sell you bitcoins anonymously; just put cash and a bitcoin receiving address in an envelope and mail it. The exchange (who you'd have to trust to actually send you the coins) takes the cash and send coins to the address. They have no idea who you are, and your identity isn't linked to the coins.
Well, it isn't linked to the coins until you forget to turn on TOR or I2P before spending coins on something illegal. Or you remain completely and utterly anonymous right up until you spend coins on something physical and have it shipped to your home address. Or you arrange to have contraband "dead dropped" somewhere, and you get arrested when you go to pick it up.
None of which have anything to do with Bitcoins, and all of which seem to me to be more likely ways of getting into trouble than somebody managing to figure out that "transaction for purchase of illegal stuff" is linked to "Gavin purchased a bunch of Bitcoins from Bobby's Discount Bitcoin Emporium" last year.