Another interesting thought is that the Russians were colonizing along the coast of Alaska. Ivan Fedorov discovered Alaska in 1732 and the northern coastal areas were colonized beginning in 1745 with Grigory Shelikhov.
If that had continued in earnest along the western Pacific coastal areas and into the interior of Northern Canada and the Great Plains regions, we might all be speaking Russian instead of English and Spanish.
The European colonization of the New World was more organized around gold and missionary work for the Roman Catholic Church.
The real quest for the Europeans was 1. gold, and 2. finding a north-west passage that would somehow make it easier to travel between the Pacific countries with spices and silk and the European countries.
I have to agree with marilynn07, but it is interesting to think that if it was not Columbus (who actually didn't "discover" America) it would have been someone else. If you are writing an essay on this topic, I think you could explore what the colonial European countries at the time were doing in the Americas and elsewhere, and how, if Columbus were out of the picture, what that might mean for the Americas. I think some of the possible changes might be how natives were wiped out by contagious diseases, warfare with Europeans, etc. If these things had not happened, the world may be on a different course of events. Think also about how early settlements like Roanoke (albeit a failed settlement), Jamestown, and Plymouth really set the stage for how this country would eventually be founded. Now take them out of the picture and change that history -- things could have been drastically different!
This is a fascinating question, and one can imagine any number of fantastic scenarios. Larger and more modernist Native American societies in North America, the Aztecs or Incas with more mechanical cultures, meeting later European invaders on a more even footing. It's pretty interesting, but the truth is things probably would not have been much different.
Educated people in general knew the Earth was round centuries before Columbus. Even members of the Medeival nobility had to learn astronomy to get around on campaigns in war, and there is no way to explain the movement of stars unless the world is round. So some European power, as soon as they had the opportunity between wars, would have sent an expedition across the Atlantic. That's what happened with Spain; having united the country and driven out the Saracens, they had the money, power and temporary respite from warfare to indulge in Columbus' suggestion. They really didn't expect much to come of it. The only major powers capable of doing so were Spain, France and Britain, the major colonial powers in the New World. So America might not have been discovered for a few decades or another generation, but I don't imagine the general course of events would have been much different.
Now, if the Spanish had been a little less aggressive and not killed off the Caribs and the native Jamaicans and enslaved everyone they found in the New World, that might have really changed things.
There are too many ifs and buts involved in answering this question.
Is it proper to assume that if Columbus had not reached America when he did, Europeans would have never found out about about Existence of America? I don't think so. Columbus was only one of the many people who believed in ready to try out the proposition that one can reach from west coast of Europe to India by sailing Westward. If Columbus had not stumbled upon America, there are very high probabilities that someone else would have. There could have been delay of ten or twenty years but not much more. When we are talking about historical development spanning more than five centuries this small delay is not significant.
So, it will not be unreasonable to assume that there would have been no significant differences in life in Europe and America if Columbus had not reached there.