The United States
If you are moving within the United States, getting your mail forwarded is a relatively easy process. Simply go down to the Post Office and fill out a change of address card; your mail will be automatically forwarded for 15 months without charge. You can also do the change of address online at USPS.com. At the end of the 15-month period, you can request an extension, but they don't like to do it and it may take some time. They do, however, give you a change of address "kit" that helps you tell your correspondents that your address has changed.
The United Kingdom
The Royal Mail forwards mail after you change addresses for up to 2 years, but only if you pay for it. Rates are substantial (39 pounds per year in 2009) and the Royal Mail requires you to present two forms of acceptable identification if you apply in person or online. You have to send your original ID to them if you apply by post and they will send it back in 10 days from when they receive it. They also have a secure online application with different identification procedures. With the change of address and forwarding, you also get a free home movers' box from an Internet partner site containing tea, coffee, snacks, cleaning products, toilet tissue and discount vouchers if you check the permission box.
The process in Canada is similar to both the United States and Britain. A change of address form can be filled out at the nearest Canada Post office or online. Be prepared to present multiple forms of identification whether you go to the post office or make the change online; they also require that you have "knowledge of your personal credit history" to assist in the authentication. Canada Post will forward in increments of 3 months for up to 12 months. Canada Post charges fees somewhat higher than those of Great Britain's Royal Mail.
The Australia Post will redirect your mail for up to a year in increments of 3 months at fees that are rather less than those of Canada or the U.K. They offer free notification service to mailers who know you with the purchase of redirection and change of address services. They require one acceptable form of ID to complete the application process.