I think the question is interesting, as there are many related issues in the ballpark that perhaps are being wrapped into it. "Control" is a very different sort of a thing than, for example, "authority" or "sovereignty". I think if we separate all three of these concepts, as they are distinct, then we can more easily answer the question of who is in control of the earth.
Control implies having ultimate power in directing the course of events. We might say that humans are the ones carrying out events, but that other entities (such as Satan, demons, aliens, angels, or God Himself) may be influencing the actions of those humans. On that scenario, those other entities would be in control of the earth. So, for example, we could say that Satan is ultimately in control of the earth even though humans are carrying out most of the actions. One may think from a verse like 1 John 5:19 that the Bible "clearly says" that Satan controls the world. (We could perhaps supplement 1 John 5:19 with 2 Corinthians 4:4 for further evidence.)
In response to this thought, I have a consideration. From the context of 1 John 5:19, John is contrasting children of God from the rest of the world, which he says is controlled by Satan (or, according to a more literal translation, evil). At that time, perhaps it would have been accurate to say that Satan was in control of the world. But, if we believe the Scripture to be accurate, then we will believe that "of the increase of His government and peace there will be no end" (Isaiah 9:7). From 1 John 5:18, we can assume that wherever (and to/in whomever) the kingdom of God spreads, Satan has no more control. It follows, then, that if Satan was controlling the world in John's time, and it is now 2000 years after John, then Satan's control has been reduced at least somewhat. That said, I don't believe we can easily cite Scripture and then conclude that Satan controls the world. (If we redefine "world" to include only the population of unbelievers, then I think we reduce our inquiry to a question that is not as interesting as the one we started with at the beginning of this post.)
Now, it is important to once again note that "control" has a different meaning than "authority" and "sovereignty". It will be interesting now to consider how authority and sovereignty play into the subject of "who has control of the earth?"
So, let's consider the subject of who has authority over the world. Someone who thinks Satan controls the world may also believe that Satan has authority over the world. Perhaps that was true, for a time (see the account of the Fall in Genesis, or the temptation of Jesus in Luke 4). But we read in the New Testament that Jesus declares that He has been given all authority in heaven and on earth, and that He gave at least some of that authority to His followers (John 28:18, Luke 10:19, Matthew 16:19). So, these days, it appears as though there is no authority over the earth left to be had by Satan. Additionally, we might consider the words of Moses in his creation story account and David in the psalms that reflect the belief that God gave humans authority over the earth from the beginning (Genesis 1:28, Psalm 115:16). Thus, as far as who has authority over the earth, it appears that God always intended it to be humans. Whether Adam and Eve relinquished their authority to Satan, and whether Jesus "won" the authority back, is another discussion.
Finally, on the topic of sovereignty, I think it needs to be clearly stated that sovereignty over the earth is very different than control over the earth. I would say that sovereignty should also be distinguished from authority, at least from the type of authority of interest. The best analogy I have thought of so far is a referee presiding over a sporting event. He does not control the plays, and he does not have authority to change, create, or interfere with the plays, but he does constrain the plays to laws, principles, and rules.
Unlike Jehovah's Witnesses, most mainstream Christians I know would probably deny that Satan controls the world. However, they may say that "God is in control". The "control" most Christians are referring to is a sort of sovereign control over everything in general, perhaps. But, to be especially clear, we might ask the further question: "If God is sovereign over the earth, does that mean that He is in control of the earth? Also, does He has authority over the earth?"
Again, I want to cite the Psalms 115 passage and point out that David wrote that God had given the domain of earth to man. It seems to me that God could be sovereign--as in, overseer--of the earth without having direct authority to intervene in earthly affairs, unless a rule was being violated. If God gave authority of the earth over to man, it would seem as though God would be usurping man's authority by intervening without man's request. So now we have a logical explanation for the role of prayer, and we can also more clearly see its importance. God cannot act on the earth without the permission of humans. God's sovereignty does not imply His authority to make changes as He sees fit. At least this is a theory that is worth considering in more depth.
So are we all doomed to the fate that is destined for human beings who exercise their authority over the earth but don't seek after righteousness (Matthew 6:33, Romans 3:11, Romans 6:23, Romans 8:19)? The answer is: no. Jesus came to save the world (John 3:17). God desires the best for humans and the earth. Scripture indicates that Jesus (a man, but also God) intercedes on our behalf (Romans 8:34). Notice here the importance of God entering into the earthly realm in human form! Now God can pray for earth as a human, and He can pave ways for Himself to enter and intervene in ways that perhaps few of the rest of us are asking.
Now I ask you: "Who is in control of the earth?" It seems to me that we have a lot more power to address our problems than perhaps many of us are willing to admit.