Yes. The Sega Dreamcast requires a memory card to save games. It uses a proprietary format called the Visual Memory Unit (VMU)—a small, removable cartridge with a monochrome LCD screen that slots directly into the Dreamcast controller.
Most Dreamcast games will not let you progress past the title screen without a VMU inserted. No save = no progress. Get at least one official Sega VMU (white, blue, black, or limited editions) with your console.