Save your American coppers from 1959 to 1981 for they contain 95% copper blended with zinc - copper that is worth over 3 cents as this article is written. You can see the current melt value of in a Cu penny at coinflation.com.
There is a growing market for copper pennies on eBay and over at realcent.org. As an example, this retailer sells copper cents by the pound.
Save your American cents from 1909 to 1958. These coins have the "wheat ear" back and in addition to being 95% copper, the common date wheat pennies are now traded between collectors for 4 cents each and up. Rare dates, varieties that are in demand, and coins in exceptional condition can sell for much more. So save the common date wheat coins up and sell them to your local coin shop or on ebay. You can also sell off any rare coins for a premium.
Save the Canadian pennies up to 1996 you find because they are even better than the US 95% copper Lincolns - the Canadians are 98% copper. Starting in 1997 Canada switched to copper plated zinc and than Cu plated steel in 2000. Canadian 98% Cu pennies are also now trading like the 95% copper US pennies trade at a premium over face.
The rest of your pennies are just worth a one cent, but don't throw your coins away either. Put your coins in a jar and when you get a bunch collected, just roll them up and return them to the bank. Some banks have coin machines, which is even better because no manual rolling or counting is required.
If you don't want to roll the pennies than at least donate them to a worthy charity because every penny counts. An old but true saying is "Don't waste the pennies and the dollars will take care of themselves." Happy hunting.