In the short term, and the perspective of the story, Tom desires the buried pirate treasure that Old Scratch, the Devil, knows the location of. Scratch will only reveal this knowledge to his "friends", meaning those who have struck a deal with him; the deal he strikes with Tom is the exchange of the treasure for Tom's soul.
Tom wants the treasure, but this competes with some other desires, such as his desire to torment his wife. This delays his opportunity to acquire the treasure and even causes him to waver in his decision, but ultimately he goes through with it. So, in the context of the story, Tom's desire was fairly shallow and one-dimensional.
In the broader sense, it's hard to say what Tom desires, in terms of his life goals and motivations. What exactly does Tom want, in the philosophical sense? This is hard to say, because it doesn't seem like Tom has a job or any hobbies, and his life is consumed simply with aggravating his wife and being miserly. One might assume that the acquisition of the treasure would satisfy his hoarding instinct, but as the story evidences, it does not, suggesting that perhaps nothing could ever satisfy Tom. In this sense, Tom's desire (to have everything for himself) is impossible, and explains a great number of his personal choices and character flaws.