Character Analysis
We'll be honest: Nearly Headless Nick is a lot more interesting in the books than in the movie.
In the books, he makes for interesting color and the presences of ghosts in general set up some reasonably big plot points. But here, he doesn't have much to do but hang around and tell the gang "Hi" every now and again. (We're glad John Cleese got a nice fat check out of it, at least.)
So why is that? And frankly, why are a number of other characters from the Harry Potter books given such short shrift? Some of it has to do with running time. Rowling could delve into certain details with the books that movies just couldn't show without boring us to tears. Harry Potter and the Sorcerer's Stone has a lot less time to play with, and it needs to more or less stick to the really important stuff without getting too distracted.
Nearly Headless Nick is the victim of that. His back-story and personality get tossed aside in favor of the central plot. He needed to be included—gotta make the fans happy— but he really doesn't have anything much to do.
But he's basically floating scenery. He's a sign that Hogwarts is full of surprises…some of which can talk (and grouse about how they were left out of the Headless Hunt again).