There's always the classic gold smuggling route. Back in the days of e-gold you could transfer wealth anonymously with no problems, all it took was sending in an international money order with a piece of paper with your account number. No ID required to send or receive, not sure how the receiving part worked as I never tried that.
The authorities in the US shut that down but it was a long drawn out legal struggle that redefined what a 'money transmitter' was, the site was around since 1996 and usable up to 2009.
It's still a very popular method but it's done in person by criminal syndicates nowadays. The golden days of your average joe being able to send tens of thousands of dollars around the world anonymously in a few hours are long gone.