There are numerous companies that offer mail scanning/destruction/forwarding services. They vary dramatically in price and service levels, so I'd suggest a bit of research into whichever one you select would be a good idea.
There is an excellent list of a number of the services including prices in this FlyerTalk post. The rest of that thread (click the thread link in the top right) has some further suggestions, but be aware that there are occasionally straw-man posts in that and similar threads (although most of them get deleted shortly afterwards).
Personally I took a different approach. The majority of the places I receive mail from (or at least, the ones I cared about) had the ability to send as an email rather than via mail, so all of my bank statements, etc all come through as emails. The remaining mail I get sent to my parents, who generally hold it until the next time I'm in the country to cull it out and find the one or two things in there that matter! Things I do require more quickly (eg, new bank/credit cards if the old one if expiring) they simply re-package and send onto me.