If you are interested in replacing the save batteries in Game Boy cartridges which may have run out, you will first need to determine which battery you need to buy to replace it. This can be checked by opening up a Game Boy cartridge with the proper screwdriver (3.8mm Gamebit). For authentic carts, the battery type is inscribed on the PCB, usually in the upper right.
The bulk of Game Boy titles require a CR1616 battery. Certain games may make use of more power-hungry hardware features in the cart, such as later Pokémon titles making use of a real-time clock. I couldn't find a reliable list of which carts used which battery, so I decided to put together my own.
The following is a list of Game Boy save batteries I've found in carts I have personally opened up and confirmed myself.
Regional variants of a game may use a different save battery. For example, Pokémon Yellow is widely reported to be using a CR1616 battery for Western releases, while I've confirmed its Japanese release used a CR2025. For this reason, I have listed the region of each game I've confirmed next to it, and do not recommend relying on this list unless you are specifically replacing the battery for the region listed here.