Pennies used to be made out of 95% copper and 5% zinc. Until 1982 that is. After that, they were made with 97.5% zinc and a copper coating. Why the change? cost cutting. Inflation made copper too expensive and zinc is much cheaper. Today, a pre-1982 penny has over 2 cents worth of copper in it. It is currently illegal to melt them down so there isn't much you can do with it. Some people do collect them and you can find them for sale on E-Bay as well as other places on the web. There have been times in the past where they have, for short periods, changed the composition, like in WWII when they made them out of steel. Zinc pennies only have about two thirds of a cent worth of metal in them.
There has been off and on talk about either making the penny out of a different, cheaper metal (like steel), or eliminating it altogether. How likely is it? I don't know, but I wouldn't be surprised to see them change the composition. I expect them to make pennies for a long time to come though. Probably people will stop using them by choice long before the mint stops making them, similar to what happened to the half-dollar. I have been to a number of stores that didn't give pennies as change, they just round up the amount the give back to the nearest nickel.
The U.S. nickel has never been pure nickel, it has always been 75% copper and 25% nickel, an alloy called cupro-nickel. For a few years in WWII there (1942-1945) they made some nickels with 35% silver. They currently have right around five cents worth of metal in them. A nickel weighs 5 grams and been has ever since it was first made in 1866. The introduction of the 5 gram nickel was shortly before the Metric Act of 1866 made the metric system legal in the United States. Canadian nickels used to be pure nickel, then they changed them to cupro-nickel, and now, they are plated steel.