Area Control is a common game mechanic in which players attempt to control areas of the board. This is common in war games, but also in pure strategy games -- Othello/Reverso is considered an area control game -- and can be an effective mechanic for games of any theme.
Games using this mechanic include, among many others, Go, Monopoly, Risk, Carcassonne, Settlers of Catan, Scythe, Small World, Eight-Minute Empire, El Grande, Twilight Imperium, Twilight Struggle, Battle Sheep and Star Wars: Rebellion.
These games run the gamut. Battle Sheep involves filling fields with sheep by running them back and forth in straight lines; it is suitable for children, and takes maybe 20 minutes to play. Twilight Imperium involves building an intergalactic empire, takes about six hours to play, and is not generally a good idea for humans of any age. Carcassonne is a free-form puzzle in which visual-spacial perception is often more important than strategizing. Go is largely recognized as one of the more strategically challenging games ever invented by humans.
While making generalizations about area control games is a losing battle, they do tend to be winner-takes-all-games (even in cooperative games like Pandemic, either the players or the pandemic will win), and they tend to involve pitting your wits against the other players. They are more likely than most other types of games to be two-player games, although multiplayer games are common as well. If you like games based on logic, strategy, and practice, this is a rich area to explore. Likewise, this is poor ground for social games, although a few cooperative games, like Pandemic and The Captain is Dead, have manged to break into the area control arena.