One of the most popular pieces I have ever written was on collecting nickels. If you type "collecting nickels" into the google search engine, my post appears on the first page. It was written in February 2011 and it still gets many hits. It is obviously a somewhat popular subject.
My thoughts on collecting nickels is almost the same as pennies, except pennies are a little more complicated. As I mentioned with nickels, it is one of the few investments that is a hedge against both inflation and deflation at the same time. The same is true of a penny.
One of the big problems is that pennies are not worth much. While they are a little less bulky than nickels, you would also have to collect 5 times as many to get the same monetary value (not necessarily metal value) as the nickel.
Pennies are also a little more complicated because the metal value will depend on the date the penny was minted.
If you find a "wheat penny" that is dated from 1909 to 1958, then it is mostly copper (95%), with the exception of the 1943 penny. I told you it is complicated. These pennies are easy to spot because the back has a design of wheat heads, instead of the current day pennies that have the Lincoln Memorial on the back. It also says "ONE CENT" in big letters. The metal content in these older pennies is currently worth about 2.5 times the face value of the coin. In other words, the copper is worth about 2.5 cents. However, some of the older pennies may be worth substantially more due to rarity.
Pennies dated 1959 to 1981 (and some 1982) are made of 95% copper and 5% zinc. These are worth more than pennies made in 1982 to the present day. If it is worth it to sort through these, then it may pay off one day. But it will take a lot of time. I would only suggest doing it if you are multi-tasking. If you are just sitting there watching a football game, then maybe spending some time sorting through your old pennies is not a waste of time. Again, currently the metal content in these pennies is about 2.5 cents, but it will vary depending on the metal prices, particularly copper. It was over 3 cents at one point.
The pennies from 1982 to the present are mostly made of zinc. Only about 2.5% is copper and most of that is in the plating. This may still end up being a good investment one day, depending on how much the Federal Reserve inflates the currency. But zinc is not as valuable as copper, so the pre-1982 pennies should serve as a better investment. Right now, the mostly zinc pennies have a metal content that is worth just over half a cent.
I understand that a lot of people think it is crazy to save pennies. Perhaps it is crazy. But you can't judge it based on what they are worth now. You could save 100,000 pennies and that would still only be worth $1,000. That is a lot of pennies to store (2,000 rolls), but the question is what they may be worth one day in the future, based on their metal value. If the Fed goes crazy with monetary inflation, then maybe the metal content will be worth $10,000 one day, or even more.
And again, even if you are completely wrong and there is no monetary inflation in the future (highly unlikely), then you can always just trade your rolls in at the bank in exchange for bills. However, I'm not sure that I would bring in 2,000 rolls at one time. You may want to split it up into a few trips.
While it is illegal to melt your coins, this probably won't matter. As I mentioned with the nickels, it is actually preferable to leave them in coin form so that the value can be easily assessed. It is the same with pre-1965 silver dimes and quarters. These are now traded at coin shows for their metal content.
In conclusion, collecting pennies is a personal choice. If you have a lot of time and some space to store them, then you aren't going to lose anything by holding them. Interest rates aren't paying enough right now to worry about that lost opportunity. But I also wouldn't spend a lot of time sorting through your pennies if your time is better spent on your career or other projects that may be much more profitable. But if you do decide to collect pennies, then you better hurry, because there will come a day when pennies will be made of steel or else they just won't be used at all due to the continuing devaluation of the dollar. Either way, expect pennies, especially those dated prior to 1982, to slowly disappear from circulation.