You could look at the Family / Clan model.

You create your first two characters as a part of two separate Families or Clans, when you get to marriageable age you create your third character (son / daughter / lizard baby etc) and keep on adding party members to the clan / family. It would follow the empire building model Luckless described, but maintain the RPG character building to a greater degree.

This could work great with any tribal / clan based society (think Vikings) where your 2nd generation characters inherit certain traits from their progenitors.

To keep the game fresh you could also build in something that I would love to see in a game - real wounds, compounding wounds, real death. Every time your character "dies" you select a wound, these start as minor (scars, lost finger, lost toe) with minor buff or debuff and grow in potency as you "die" more often until the only wounds left to choose from are crippling and eventually mortal. For eg. you might get a scar, then a bad scar then eventually frightening scars. Frightening scars would give you a buff in intimidation and possible constitution, but a debuff in charisma and make people either afraid or hateful of you.

Further "random" game events can keep the game play going in perpetuity. You would have to define a large number of these and pre-script them, but to occur at random locations and random times to keep it from feeling like you're just grinding or repeating the same old over and over.

Incidentally, I find that ending a good rpg game is much like finishing a good book. You just wish it would have gone on longer.

I've had a similar idea for a (theoretical) MMORPG for a while now. When you reach "maximum level" you can breed and create a new offspring character to play. Doing this gives (at least) 2 advantages:

1) The old character can now level up further, but has perma-death:
This would allow for high-risk/high-reward play such as going after a legendary treasure that can be handed down in the family until it breaks. The dungeon holding the treasure would be far too difficult for normal characters to attempt.
There are other ideas such as having the older characters retire as trainers in your clan village, where the higher level they reach post breeding increases their teaching rate, so you would have to trade off training speed vs risk of dying and wasting that potential.

2) The child character can get new abilities unavailable to the parent:
My game idea is loosely based on the Naruto world, where characters can master individual elements that they have innate talent for. So if your old character could use water and you breed with someone who can use wind there is a small chance that the offspring can get a new talent to combine both water and wind to manipulate ice.

Crusader Kings 2 is pretty much what you've described. You build up your dynasty through the ages. When your character dies you take over his heir's character, who is now the new head of the family. It's a sandbox game, meaning you set your own goals... there's a dynamic world going on with hundreds of AI controlled characters with their own personalities and ambitions going about their business. You turn up and you can do whatever you like to improve your family's power and reputation: climb the political ladder through diplomacy or violence, become an merchant prince and form a capitalist empire, lead your nation on a holy war, get one of your family member into the papacy... the list goes on.

The keywords you are looking for are "open world" and "sandbox". There's a lot of such games out there, but they are not well known. You can also try Dwarf Fortress, Unreal World and Patrician 3. Each of those takes a different approach and can help you find more specific games of the genre you may like.