I agree with the consensus that Blue Velvet obviously merited inclusion -- the photography perfectly captures both the sunniness of the movie's idyllic portrait of small-town America, as well as its descent into gruesome film noir.
Star Trek IV's nomination is a bit like that Cinematography nod for that one Harry Potter movie -- a long-running franchise that had never contended here suddenly pops up in this category for no apparent reason. I'd say The Voyage Home is a better-looking film than some of the grisly '70's nominees, but it's still a fairly random citation. (Though it couldn't have been totally out of the blue, seeing that ASC nominated it, along with -- gulp -- The Karate Kid II.)
Peggy Sue Got Married definitely isn't win level, but its cheery rays of sunshine bring out the movie's sense of nostalgia for a bygone era, and the moody lighting of the freemason scenes at the finale guides the story's tip into full-on supernatural fantasy. The other nominees are more visually sumptuous, but this is acceptable as a nominee.
A Room With a View in general has a radiance to it that makes it feel less stuffy than many great literature adaptations, and you'd have to praise the cinematography for its role in accomplishing that. From the painterly compositions in the city-set sequences, to the pastoral shine of the countryside scenes, the images are winningly romantic throughout. I'd probably say Art/Costume Design wins are enough to recognize this film's beauty, though.
I'm a bit surprised that no one (so far) has gone with Platoon, because it's a very well photographed film. The cinematography does a striking job of capturing the elements -- dust, smoke, fog, rain, fire -- that fill the characters' environment, giving the viewer a strong sensory impression of what life in a war-torn jungle might feel like. And of course, this movie does have the single most iconic shot in this lineup -- Dafoe dying with his hands raised. Precious Doll does have a good point though -- it does share a similar visual look as Vietnam films that had come before, though I do think few used their images to as strong a dramatic effect as this one does.
Given how integral cinematography is to the greatness of so many movies, it's pretty rare for me to vote for a film in this category that I flat don't like. I'd certainly hear the argument that The Mission's images aren't in service of a very successful movie. And I'd also take the point that a locale like Iguazu Falls is so naturally photogenic it'd be hard to screw up making it look great. But it's hard to deny that Chris Menges isn't doing impressive work here -- from the sheer beauty of the lighting, to the elegance of the compositions, to the rich use of depth of field, the entire movie is one great photograph after another. Occasionally I must acknowledge that pretty pictures can be their own artistic triumph, even if the story surrounding them is not, and give my vote to The Mission.