I thought Captain Cook was an excellent person who had contributed greatly to mapping the world, but then I came across this image.
http://i.imgur.com/4UL5cIf.jpg
Did he exploit the Hawaiian people or anything else immoral?
By the standards of European navigators of the era, Cook wasn't unusually prone to violent encounters with indigenous people. But I also don't like to characterize historical figures -- especially those as complex as Cook -- as heroes or villains.
Cook's poor reputation among people with a particular political orientation -- say, some indigenous sovereignty activists -- comes more from the way in which Cook symbolized the colonization that followed his "discovery" of Hawai'i rather than particular actions Cook himself took. Among other groups, Cook is remembered as a key figure in adding new portions of the world to European maps. Cook also brought along scientists (like Joseph Banks) and artists who conducted research and produced images during Cook's voyages. This information was added to European understandings of Hawai'i, Australia, the Pacific, and other locations. In many ways, both views are correct.
Of course, the addition of that knowledge to the European canon is also problematic in some ways, as future colonizers with deeper knowledge of a place like Australia or Hawai'i are then on firmer footing when seeking to colonize that space. Joseph Banks, for example, specifically advocated for the colonization of Australia following his voyage there. Cook's facilitation of knowledge gathering didn't only advance European knowledge, in other words, it also provided a foundation for later imperial efforts. That's important, and a key process that both Edward Said and Michel Foucault have described (in different ways) as knowledge power.
If you're interested in the specific incident that caused Cook's death in Hawai'i, that's very complicated -- and the subject of one of the best known debates in anthropology during the 1990s. The debate was between Marshall Sahlins and Gananath Obeyesekere. Sahlins argued that Cook's arrival in Hawai'i incidentally coincided with a festival in celebration of the God Lono during which Cook and Lono were conflated, and that his conflict-filled return to the island soon after was related to Cook's mismatched fit within this Hawaiian mythmaking. Obeyesekere argued that Sahlins was too quick to assume Hawaiians' deification of Cook, and that this sort of projection (a European mythmaking about Hawaiians) said more about the European imaginary of the Pacific (and "the native" more broadly) than to Hawaiians themselves. I can't do justice to the debate in such a short space, but this book review might help.
I suppose it might be helpful to think of Cook as a figure similar to Columbus. Both flawed figures to be sure, but figures that are often remembered for opening the floodgates to waves of later colonization with which they themselves weren't necessarily directly involved. That is to say, European colonization of Hawai'i and the subsequent violence enacted here may well have happened without Cook. But he did set the process in motion.