Christophoro Colomb:
Despite not knowing where he was going or what he was really doing, he changed the whole world's awareness of each other and that is important. The one real accomplishment he is deserving of is his recognition of the usefullness of the low lattitude trade winds in the age of wood and sail.
Marco Polo:
Marco Polo didn't really discover anything. People in Italy always knew China was out there somewhere. What he did change is how much they interacted and what value there was in going there. His trip to China did everything from bring the first major introduction of gun powder to Europe to introducing the ever present noodle to Italian cuisine.
Vasco de Gama: The man who led his crew to finally prove the world was round. Regardless of cultural relativism about who discovered who, NO ONE had ever pulled that stunt before.
James Cook: Another man who really didn't "discover" a thing but established contact between the western world and a larger group of incredibly diverse cultures than anyone before and after.
Roald Amundsen: Again here's a man who never really discovered anything, but out of a list of several Artic/Antartic explorers, he set the most records and covered the most ground. Shackelton had a better story, Peary was the "first" (supposedly), Scott was the major tragic hero, but Amundsen was the man who kept attention on exploration of the farther reaches of earth on people's minds the longest which is why he belongs on this list.