It depends on the system
Pong: N/A
Atari2600, Lynx, NES, SNES, N64, Gamegear: No, it's a chore to take the carts out and put them away again. The boxes will be damaged by repeated use anyway.
Vectrex, Saturn, Dreamcast, PS1, PS2, PSP, Xbox360: No, bootlegs don't deserve their own cases
GameCube, Wii, WiiU, Master System, Mega Drive, PS3, Xbox, Xbone: Yes, they're convenient and protect the games.
Gameboy, Virtualboy, GBA, DS, 3DS, Vita: Yes, but they are stored away and games are kept in a single cartridge wallet for convenience.