I'm a little late but I've been using a service called PayTrust for over seven or eight years now. They were later bought out by Intuit (think Quicken) so it's a solid company.
Basically they give you a BOX XXXXXXXXXX address. It's not a US Postal PO Box so it gets by some of the "No PO Boxes" rules some businesses have (credit card companies, etc).
All my mail goes to them, they open the mail, scan it, and post the PDF's online. The service is intended for bills and other financial docs. You can link up your bank account to pay your bills right from their interface.
The best part is that when my credit cards expire and I receive a new one, they put the card in a new envelope and ship it to my current address.
The things I don't like about the service are:
1. I paid off my car years ago. Quit sending me notices that you didn't receive an expected bill from them!
2. For whatever reason every single month they send me a notice saying my ABC credit card bill has arrived. Then I get another notice saying that a bill arrived that they couldn't assign. When I go to their website, it's the same bill. Same thing every month for years.
Other than those two annoyances, a pretty good service and for the $5 or $6 I pay per month, well worth not having to sift through a mountain of inserts for crap I don't want.