Making the Case For Short Games
Gamasutra has a feature up entitled Making a Case for Short Games, in which the author argues that a good short game is far and away preferable to attempt than an epicly long game. From the article: "Which would you rather play, a computer game that takes forty hours to complete or one that lasts just a few minutes? Don't be too quick to answer. The former asks for a serious time commitment. The latter says come and go as you please. One is a ball and chain. The other is a 'Get Out of Jail Free' card. Well, it's not exactly that bad but considering all of the things you have to do today, which type of game do you really have time for? Also, isn't it peculiar that when you complete a complex or lengthy game you rarely want to replay it, yet short games are often endlessly replayable? "
In other words... Animal Crossing! I don't think there's any other game which fits your description more perfectly. In fact, you MUST play it over the course of at least "a friggin year" if you want to take part in all the cool holidays and special events.
Of course, the story is a bit weak...