Kingdom building and Domain management is on my list as well (I'm adapting Colville's stuff as I get it to fill this)
Same with running a business or owning land for a house.
I like stuff like this because it ties people to game world, and "save the village from marauders" is a mission only as important as the village is. "Save the village your house and servants are in" is much more immediately important.
Tying into that is a crafting system. For potions, poisons, food, equipment, ect ect ect.
Again, it makes the world feel more real, and my players love taking things and making things. It feels more empowering for the alchemist to be able to brew their own potions than to go to a clearly inferior fellow alchemist and buy their stock.
And, frankly, they should be able to make wealth this way. If characters such as merchant princes, master carpenters, and fammous artisans are going to exist, they need to be able to ply their trades into making that wealth and status. I know some people worry about players not adventuring if they can make more money being crafters, but I've never found adventuring for cash to be particularly exciting.
I do like the idea of making "social combat" a good choice. I've played in a system where you can have an argument that is a mental combat. I was able to run that to allow players to badger a suspect into admitting his fault. It was a wonderful moment to give them that tool.