Soak your pennies in ketchup to clean them like new. Well, after you wash the ketchup off, that is. The salt and acetic acid in vinegar do the trick.
Hot sauce, like Tabasco or taco sauce, also will remove the oxides off pennies. As in ketchup, salt and vinegar are both in hot sauce.
Coke and off-brand colas will quickly remove the tarnish. Just don't drink the coke afterward. Coke contains phosphoric acid that cleans the oxides.
Try a variety of citrus juices to see which works best or simply let your pennies soak in lemon juice. Citric acid works similarly to the other acids.
Use a common pencil eraser on your pennies to remove the oxides like mistakes on paper. This takes more work than the others, however. The friction does the work.
Make a solution of vinegar and salt and let the pennies soak. The acid in vinegar, like in citrus, is what really takes the tarnish away.