The most important negative consequences of Columbus's voyage were the consequences that it had for the Native Americans. They were hurt both in the short term and in the long term by his "discovery" of the Americas.
In the short term, the voyage (and the ones that followed) caused various of the Indians to essentially become enslaved. They were, for example, forced to mine gold for the Spaniards. This was certainly a major negative consequence for them.
In the long term, things were worse still. With the coming of Columbus came epidemic diseases. Europeans and other Old World people had some immunity, but those of the New World had none. These diseases decimated the Native American populations as disease spread throughout the Americas. This was surely the worst consequence of Columbus' voyages.