I think someone could come up with a business plan around this: truly private garbage collection. You don't put the trash out at the corner, but contract with the garbage collector to pick up the garbage in your yard, with some sort of contract that the garbage is still yours until properly incinerated, and the collector would dispose of it in a way that guarantees privacy - incineration.
Well actually, there is - Recall.com and Iron Mountian document storage companies. In addition to document storage they both offer document destruction services, including computer media. It's aimed at businesses - but a residental user simply can call for a quote.
As I've seen from some of the privacy advocates - shred any piece of paper that has your name or other personal information on it. A home sized shredder can be bought at Office Depot or Staples - and there's nothing more statisifing than putting junk mail through it. Simple enough - sort the trash for organics, cans, bottles, etc. and shred the rest. Then if someone does want to pick through your garbage to find someting - all they get is shreds.