When one of my kids was in the hospital for an extended stay last summer, we bought him a Nintendo DSi, and we helped his older brother get one as well. One thing I noticed as they played each other's games was that game saves were stored on the cartridge, not on the DSi's internal memory. The other thing that I noticed was that games limited the number of saves they would support to a very small number. Whether it was by intentional design or merely as a function of the amount of data saved divided into the amount of flash memory that it is cost-effective to install on a cartridge, the result is the same.
The result is, because, for example, the Pokémon games only support saving a single game, and because the game is saved on the cartridge, my kids are not able to share those game cartridges with each other. They can only share cartridges that happen to have more than one save slot in them.
Now, as it happens, the Pokémon games aren't as big of a deal. Each boy having his own game is a benefit, because being able to play at the same time, and trading pokémon with each other, is a key feature of the game.
However, not all games directly benefit from having two copies. One of my boys recently got a copy of Drawn to Life: The Next Chapter, and it was only after he started playing it that we discovered it only has a single save game slot. This is contrary to the first Drawn to Life game, which, because it has more than one save slot, my kids are able to share back and forth and play their own save.
Probably the most annoying part of this whole situation (aside from the fact that there's really no reason for this considering the game console itself has plenty of storage for save data, and it would even be cheaper to make without requiring flash memory on every cartridge) is that there is no way to know the save slot situation ahead of time. Nowhere on the package does it say how many save slots are on the cartridge, nor could I find a convenient website that lists games with the number of save slots they have.
It's rather annoying that such a critical piece of information for building a library that's intended to be shared between two users is effectively completely hidden. It almost makes me wonder if this situation isn't intentional, to prevent people from sharing games, to try and get people to buy more individual copies.