The best soft drink to use to clean a tarnished penny is Coca-Cola. This is because of the phosphoric acid that's added to Coke to give it a sharper flavor also dissolves the oxides on the penny that make it tarnished.
When brass or other metal alloys become tarnished, it's because of a chemical reaction taking place between one of the metals in the alloy and the oxygen in the air around it. When metal atoms combine with oxygen, they form oxides that give the metal surface its tarnished look. Acids reverse that process, and Coke, although only mildly acidic, is still strong enough to dissolve those oxides that we see as a tarnished surface. When the oxides are gone, what's left is the shiny metallic surface.