Animal Crossing Series

Originally released on the N64 in Japan, this self-styled "communication" game gives you an empty house and a town to explore. You don't have a goal other than the goals you make for yourself. Go fishing, buy some furniture, pay off your mortgage, collect fossils for the museum, run errands for other villagers, write a letter to a friend... it's up to you. The game uses an internal clock that changes your town depending on the date and time. If you play late at night then it will be night in the game, or if you play on a national holiday then you may find a celebration going on somewhere in the town.