Honestly, I'm not sure there is a good answer to this question. Cyber criminals too struggle with it, as demonstrated by this enlightening Microsoft research paper. It focuses on how criminals manage to cash-out stolen credit card numbers, and one of the main hurdles they have to face is finding a way to receive goods anonymously.
Their solution is to hire unsuspecting "mules" and trick them into forwarding packages (incidentally, the mules are the ones who end up taking the fall). Maybe you don't want to go that far. I hope you don't.
The truth is, it's hard to have a private mail drop because most governments don't want you to have one (rightfully so). Here is a drop down of possible solutions (for the sake of brainstorming), all of which I certainly wouldn't advise trying:
- [Possibly illegal] Find a CMRA that looks shady enough not to respond to law enforcement requests, but still legitimate enough to forward your mail. Some services located in tropical islands offer a full package: mailbox, fake residency certificates and even the creation of a front company. They're a Google search away.
- [Possibly illegal] Skimming through craigslist may occasionally turn up people renting mailboxes. Are they allowed to do so? Should you trust them? I have no idea.
- [Absolutely illegal] If you have basic lockpicking skills, it may be possible to hijack the mailbox of an unoccupied flat. Of course, this is nowhere near "reliable"; you never know when the flat will be sold/rented, and some suspicious neighbor could simply call the police.
- [Absolutely illegal] The "mule" thing. If you were ready to go to such lengths, you probably wouldn't be asking such questions here.
That's all I can think of. Once again, it's nice and fun to ponder on such problems, but doing anything more than thinking about it may well get you into serious trouble. Don't cross that bridge :)