The Ending - SPOILERS

Some people posting here suggest that Miles died 'of fright' but that seems preposterous to me. Who dies of fright? Miss Giddens was pushing him, hard, about whether or not he could see Quint, and trying to get him to say Quint's name, but that's hardly a reason to just up and die. Prior to that Miles fell when he ran from the house, but he fell on grass, so the idea that he cracked his head and/or induced something like a stroke or brain hemorrhage seems very remote.

We the viewers see Peter Quint standing amongst the statuary above Giddens and Miles, with his hand outstretched - and then Miles dies. So the most likely conclusion is that Quint takes Miles' soul. Giddens was trying to 'exorcise' Quint by having Miles say Quint's name (why that would work, I don't know, but I'm no expert on exorcisms), and she seemed to believe that if Miles would just say Quint's name, that would serve to banish Quint forever. If that was actually true, then Quint taking Miles' soul at that moment makes sense, as it would be a 'now or never' moment for him. Take the child now, or be exorcised forever. And Quint standing there, with hand outstretched, followed by Miles' collapse and death, to me indicates Quint caused Miles to die.