If Columbus had not discovered Americas someone would have found it sooner or later. However, modern world would be drastically different if the contact proved to be a little different.
Spanish colonization of Latin America went at a lightning speed due to two very fortuitous events one benefitting Cortes (Aztec) and Pizarro (Inca). Within 40 years of Columbus landing - two of the greatest empires were gone. This lightning change gave no time for the natives to get immunized to Eurasian diseases and learn their technology (especially metals). The native empires were strong and advanced enough to learn these given enough time. Time was not on their side. Incas were hit right at the time a major epidemic was ripping through them. If Pizarro landed a century later, it is possible that the few survivors of the epidemic would have been able to repopulate the fertile region giving the Europeans some challenge.
If instead of Columbus, a number of other explorers from nations with less religious fervor came and open to better working with native empires, it was possible for the native civilizations to have survived much longer. For instance, colonization of India took centuries and India came out of the colonization intact. The natives would have learnt and might have begun their own voyages.
If Americas were discovered a couple of centuries late, then there might not have been a massive deluge of migrants from England in the 16th and 17th centuries fleeing religious persecution. That might mean that modern US and Canada might not be English speaking and neither might have English become world's lingua franca.
If Spain didn't get such a rapid access to Latin American gold and silver, European history would have also been quite different as Spain might have sooner surrendered the dominant power status to Britain and France. If the Latin American silver didn't flood the European markets, it would have been much harder for European colonial empires to have formed elsewhere. With a much different form of colonialism, world would have been very different.
Depending on who eventually discovered Americas and when it was discovered, world history would have been quite different