I’m sorry, I failed to pay close enough attention to the question and I did not focus on the Americas. Much of my answer is still the same as what I said above. Let me expand on the last part of my answer.
I would say that the Americas would be at a much lower level of technology and wealth if no Europeans had ever made it to the “New World.” I have no doubt that the Native Americans would have improved their technologies by now, but they would have had some serious disadvantages nonetheless. For one thing, there would be no draft animals in the Americas. There would actually be no large domesticated animals at all with the possible exception of the llama. This would mean that agricultural production would not have taken off very quickly because there would have been no animals to help with plowing. Transportation would have continued to be by foot unless the Native Americans had made the leap from carrying or pulling things to creating automobiles. There would have been no wagons or other conveyances to serve as intermediate steps. This alone would have slowed American economic development drastically.
The other big thing is that none of the European technology would ever have made it to the Americas. The Native Americans would have had to create all their technology from scratch. When Europeans came, the Americans were at least 1000 years behind in terms of technology and there is no reason to think that they would have caught up by now. Presumably, then, the Americas today would be at least 1000 years behind Europe in their development if somehow the Europeans had not made it to the New World.
There are a number of ways to understand this question. Let us examine two of them.
First, the question could be asking what would have happened if Christopher Columbus, the individual, had not sailed to the Americas. If this is all the question is asking, I would say that there would have been no appreciable difference. If Columbus had not made it to the New World, some other European would have done so very soon. Columbus was not the only European explorer and it seems unlikely that he was the only person who could have come up with the idea of trying to explore to the west. In this view, Columbus is not really important. He simply happens to be the European who chanced to be “first” to the Americas and there are many others who could have had the same effect that he did.
Second, the question could be asking what would have happened if Europeans had never discovered the Americas. This is, in my mind, a completely unrealistic question. The Europeans would have inevitably discovered the Americas because they were bent on exploring and exploiting areas outside of Europe. They had the desire to explore and the technology to fulfill their desires and they would have found the New World.
Now, if we are supposed to imagine that somehow it was impossible for Europeans to reach the Americas, we really would have a very different world. First of all, it is likely that the world would be less democratic. I would argue that the American Revolution helped make people more aware of democratic ideas and that, without the presence of Europeans in North America, there would have been less of an impetus for democracy. Second, I would argue that Africa would be better-off. If the Europeans had never made it to the Americas, there would have been no reason to take millions of Africans as slaves for the plantations of the New World. Finally, I would argue that the world would be less wealthy. The United States has the world’s largest economy now, which it would not if Europeans had not come to the New World. If the Native American societies had developed on their own, they would eventually have gotten more technology, but North America could not possibly be as prosperous as it is now. The Native Americans would have been starting more or less from scratch and would not have achieved as much as people in the United States have with their infusions of knowledge and technology from Europe. All of these things, and many more, would be different if in some way the oceans were impassable and the Americas had never been “discovered.”