pull up your mailbox. they will eventually stop delivering, and all mail will be returned as moved with no forwarding address ... i know this to be true because after receiving over 70 POUNDS of junk mail in a SINGLE WEEK, i finally took down my mailbox in 2000, and have cheerfully been mail-free for well over a decade. USPS doesnt like it, but thats ok, they dont HAVE to like it. although i DID have to file vandalism and littering charges against the USPS several times for leaving bundles of mail on my doorstep before they finally stopped.
i also had to make the case in court (which i did, successfully) that there is no legal compulsion or requirement for any individual to accept postal mail (which came up as a result of a failure to appear charge from not receiving a jury summons) nor is there any city code (where i live, your case may be different) requiring the presence of a postal mail box on private property. like the USPS, the court also didnt like it, but that is why they have process servers to hand deliver summons.
regarding an early answer suggesting the utility companies wont like it... it is true, they dont. and even if you keep paying them, they may turn off your service if they receive multiple bills returned to them... however, now that all utilities (that i am aware of) offer electronic billing, this is not an issue. and even when it WAS an issue, speaking to their billing department about your situation usually will solve the problem, and contacting a lawyer to send them a nastygram about it has always worked where a friendly phone call didnt.
in 2000, most people thought i was crazy to do this, but i always told them i was just ahead of the curve ... i believe that the last 15 years have shown this to be true.