If you want an immersive, elaborate game that can last months or even years, then you want a Table Top RPG or role playing gaming.
Normally one player is the game master who sets up the world, the conflict, and runs the game. Everyone else creates a character that they act as. Most RPGs have printed guidebooks explaining exactly how to play and the rules can range from very elaborate (detailing how much weight you can carry, how quickly your supplies spoil, and how often you characters must eat) to relatively simple (what's your health, what are you abilities, and how you can fight). Game themes can put you in space, in a fantasy world, or make you a small mouse depending on what game you decide to play. In these your imagination really is the only limit.
But be prepared to dedicate a good chunk of time. There are games that have run for years, and it's not unusual for groups to play for over four hours at a time. It also takes time to go through the rule books and make sure you have it down. There's a reason it's commonly said RPGs are the only games where walking 3 miles can take 30 seconds but a 30 seconds fight can take 3 hours.
The classic RPG is Dungeons and Dragons, but there are more. Click here for a list of the RPG manuals and books about RPGs in The Urbana Free Library.
If you still want a board in your board game for your RPG, then Mice and Mystics is the game for you!