Video games create fantasy space in which we play. These are often enjoyable because they are an escape from everyday life. Some, however, want to become a part of our day. One way they do this is to make things happen in the game in accordance with the time (and sometimes date) in the real world.
This can be games like The Longing or Animal Crossing that tie events in the game with the passing of real world time. Maybe you have to wait for a certain number of hours, or maybe you need to come back at a certain time of day. Either way, your in-game play is linked to the real world by the hands of time.
Other games use the real clock to reward you for not playing. Neo: The World Ends With You for example, offers certain types of pins (upgrades) that level up the longer the game has been off. Games like Pokemon have creatures that change form based on the season on your DS clock. Cozy Grove is synced to real world time, and provides 30-60 minutes of new quest content each day.
Mario Party 6 has certain mini-games and game boards that are different in day and night. The Legend of Zelda: The Wind Waker's start-up screen varies depending on the time of day you were playing. In Simpsons Hit and Run, during Halloween, Christmas, Thanksgiving and New Year in the real world you get game characters dressed up in a special outfit. Simpsons Hit and Run also has a different start screen depending on whether it's Christmas or another holiday. Finally, how about Superbrothers Sword & Sworcery EP that uses the real world lunar cycle so that certain puzzles can only be completed during a full moon, and other elements only during a new moon.
This is a novel thing for games to do. It's also quite useful for families as it means you are usually limited in what you can do in a game in any one day. These games encourage players to pop in for 30 minutes or do, do their tasks for the day, and then leave until tomorrow.
This list includes 19 games from the last 25 years, with 408 likes. They come from a range of different genres and play-styles and are all good games if you want to sync play with real world clock.