The Sega Saturn was one of the first consoles to feature a built-in real-time clock. Most systems now have one, so I’m kind of surprised that very few games make use of it. Animal Crossing does, sure, and some Pokemon titles have time-of-day features (which they had to include their own clocks in the cartridge hardware to support), but few other games bother reading the date.
One prominent example of a game that did was the Christmas demo version of Nights Into Dreams. Ordinarily just a single-level of the full game, the disk had a number of special modes that would crop up at different times. December was one of them, which triggered Christmas Nights mode, with special cutscenes and graphics. But it also had special events for playing during November or January (“Winter Nights”), New Year’s Day, and April Fools’ Day. Especially notable was an unlockable mode that allowed playing as Sonic the Hedgehog, in what is his first true 3D outing!
This video shows off all of Christmas Nights Into Dreams’ special modes, and you don’t have to fiddle with your computer’s clock to see them!