Several characters in Gatsby could be characterized as selfish, either is a material or spiritual sense. Tom seeks to maintain both a wife and a mistress without consequences and without losing the love of either. Daisy on the other hand, is portrayed as too impatient and spoiled to wait for Jay to return for her, marrying Tom only because she herself wanted her future decided right then and there.
Throughout the novel, Tome displays a rather distasteful selfish trait: greed. Even though he purportedly can't stand Daisy, the idea of her seeing anyone else (while he is already cheating) infuriates him. He wants the people in his married life to sit around and wait for when it's convenient for him to acknowledge their existence whilst he runs around with other women, and the idea that they could get along independent of him fails to register in his mind.
Daisy is selfish in a slightly different way. She acts spoiled and impatient, and makes a snap decision without considering the consequences for others. She "want[s] her future decided right then and there, and by some for- love, money, practicality". This leads her to marry Tom, despite having promised to wait for Gatsby. This selfishness actually serves as the catalyst for the entire action of the plot, as it was Gatsby's failure to reach his goal of Daisy's love that draws him into the bootlegging business in the first place, and his conflict with Daisy's husband that eventually brings about his downfall. Had there been no fight in the Plaza Hotel, Daisy wouldn't have tried to sooth herself by driving, wouldn't have hit Myrtle, and Tome wouldn't have had the means nor the motivation to send a vengeful Wilson after him.