I can't think of a proper term for it but lately I'm into games that lets you expand your territory like inFamous and Saints Row: The Third and if I recall correctly The Godfather: The Game. What other games are like these?
Civilization V should be an obvious one. Same with other war based strategy games like StarCraft II. But I figure you're talking about this on a larger scale and not single games...
The World Ends With You is kinda like that where you can dominate specific regions of Shibuya with a fashion style of your choice, which affects your equipment's stats and such.
Assassin's Creed III is like that. Liberating cities and then being able to recruit assassins as a result.
Tokyo Jungle is like that, albeit on a smaller scale and not the same kind as the others. You mark territory and when you "own" a zone, you can then mate.
If I recall correctly, Grand Theft Auto: Vice City was similar to that.
It was San Andreas not Vice City, though I found the mechanic in San Andreas annoying since if you expanded your territory you were constantly getting notifications about turf wars.
Does Risk count? :P
Edit: The Contested Territory concept page might be of help
You can basically buy whole cities in the Assassin's Creed II trilogy.
I don't think that you really controlled territory until Brotherhood though, I could be wrong but that's how I remember it.
Oh yeah... II just had the villa stuff.