Of course! No reputable villain or Imperialistic Global Superpower would set their sights on anything less than World Domination®! As Evil Plans go, world domination is ambitious, more logical and sometimes easier than wanton destruction of everything. They want to be in charge of everything and everyone. Usually the motive is just to feed their lust for power, their massive egos, and their Greed, but sometimes they've got somewhat twisted ideals that they want everyone else to adhere to and world domination is the Path to a Better Future. Or it's just because they are dicks.
Either way, this ambition will put them in direct conflict with the heroes, whether professional or "I just want everything to go back to normal" types. Usually said villains fixate on the hero or someone/thing close to them as being part of their master Evil Plan. For a villain who has finally acquired godlike power, and did not use it to Ascend to a Higher Plane of Existence or euthanize the universe, then this is the next logical goal and use for said power.
Villains who want this will occasionally combat other villains who want to destroy the world or use it for other purposes, and sometimes, just sometimes, team up with the heroes to do it. After all, you can't conquer the world if it's destroyed, right? Whether or not the villain attempts to stab the heroes in the back the instant the world is safe, or they nod and civilly go back to their Secret Lairs in a gentleman's agreement to face each other tomorrow depends on the villain.
The result of world domination is sometimes subverted, parodied or deconstructed when the villain actually succeeds, and it turns out that ruling the world isn't nearly as gratifying as they thought it would be — exactly what does one do with the world once one has it, after all? As any immortal would tell you, ideas to try for the world (whether utopian or dystopian) can be limited. Plus, once you're ruling the world, you literally have to be in charge of everyone, and that's like herding giraffes. Seven billion giraffes, as a matter of fact. You actually have to run things, and make sure it works, and dang, Dystopia Is Hard. You will end up snapping or getting crushed under the workload of trying to dictate everything. If they did it with Mass Hypnosis to get rid of The Evils of Free Will, then it'll be considerably easier to rule... and so dreadfully boring they undo the whole thing just to have someone to talk to. No wonder that "illogical" world destruction has an appeal that competes with world domination.
The more fleshed-out villain will have some specific perception of what is wrong with the world and believe that a strong central authority with vision and strength of purpose can set it right.
For more information, check out the Evil Overlord List, a detailed guide on what an evil overlord should and should not do. Typically, this is accomplished with Stock Evil Overlord Tactics. Although sometimes the plans of villains with this motivation go rather in the Missing Steps Plan direction.
There have been several country-specific SubTropes which have been popularized in Western thought and media, each country taking its turn to be the boogeyman for a few decades. These would include:
Alternate-History Nazi Victory, which was a fear during World War II. The trope became even more prolific after the regime's atrocities came to light, making it a good premise for a Crapsack World. A lot of the fear from this trope also drew on the fears of a pre World War I Imperial Germany taking over the world. In any case, once the World Wars concluded, a new superpower would set up itself as a contestant for world hegemon, which would be...
Russia Takes Over the World, which was popular during the Red Scare in the 1950s and 1960s (and saw a resurgence in the 1980s as the Cold War heated up again). The advent of detente however led to...
Japan Takes Over the World, which was influenced by Japan's powerful economy that emerged in the 1970s and the spread of its pop culture in the 1980s, and was especially popular in early Cyberpunk stories. However, this time it was about economics and not military and political espinoage. The lost decade of Japan in the 1990s which led to an economic and production standstill has led to another East Asian superpower filling this role, which would be...
China Takes Over the World, a concept that has gained influence in the 1990s with the rise of the Chinese economy and manufacturing. The economic liberalization and large population which has also made the Chinese an influential target for corporations and movie studios back this claim alongside China's powerful army. With a recession in the 2010s and an increased desire to perpetuate a trade war to avert this trope however, this trope may now be discredited even with China's overall economic growth taken into account.
America Takes Over the World, which has generally always been a concept people in the post-World War II era have entertained, especially in the post Cold War world with USA being the sole superpower.
Eurabia: Fundamentalist Muslims take over Europe if not the whole world and turn it into a repressive theocracy. The United States feared a variant of this trope post 9/11, but the refugee crisis from the Middle East in the 2010s led to renewed fears of this in Europe.
See Take Over the City for a more modest version. A Villain World is a situation where this actually happened (for absence of a hero or some other incident that granted the bad guys absolute power) but a hero emerges and begins to undo the damage from the inside. For the opposite, see Save the World.
