You need someone to check your mail for you, so the most convenient option might simply be to use the mailing address of a close friend or family member whom you trust, ideally in the same province/state/region as where you lived before, in case it matters for certain things like driver's licenses and such.
Alternatively, it might make sense to get a post office box from your country's postal service, although you will need to arrange someone to check your mail for you.
Finally, there are commercial services that will accept mail deliveries for a fee - as DJClayworth points out, often called "virtual mailboxes". Some even will open your mail with your permission, and scan it and send the contents of documents to you.