We can see Nick Carroway change in various ways over the course of The Great Gatsby. Many of Nick's changes relate to his relationships and his views on the people in his small circle of friends.
Nick carries on a rather bloodless romance with Jordan Baker, believing that he will marry her. The two share a sense of ironic distance from the rest of the upper class set that gathers at Gatsby's parties. This ironic distance, in the end, proves to be temporary for Nick but not for Jordan. While she maintains an emotional distance from Gatsby and his tragedy, Nick grows into a sympathy for Gatsby.
In this sympathy, Nick almost comes to identify with Gatsby, coming to think that Gatsby was the best of the whole lot, worth mourning when he is dead. As he was at the opening of the novel, Nick would have probably belonged to the ranks of those who refrained from attending Gatby's funeral. However, due to his changes in feeling and his expanded ability to withhold judgement, Nick ends up organizing the funeral.
This last change may be the most important one for Nick. Learning to be honest and to see in himself the negative qualities that he sees in others, Nick finds a maturity that he did not possess when he moved to the east. Though this is a maturity that does not characterize Gatsby, it serves to bring Nick closer to Gatsby. He begins the novel like Tom and Daisy, but ends identifying with the wealthy bootlegger.
At the novel's end, most readers find that Nick is more akin to Gatsby than to any other character in the book.