What has no use at all in the future portrayed in The Time Machine?
There are several possible answers to this question, and the answer provided by jamie-wheeler is the best one if you are talking about the themes and meaning of the novel. I thought I might give some very specific things that were no longer needed.
In Chapter IV, the Time Traveller is still trying to figure out what happened to humanity, having just met the Eloi. In noticing that there are no differences between the sexes of the Eloi, he postulates that "where violence comes but rarely and offspring are secure, there is less necessity--indeed, there is no necessity--for an efficient family, and the specialization of the sexes with reference to their children's needs disappears."
There are several other answers that also come to mind as the Time Traveller explores the future of mankind. When he goes underground, he notices there's no longer a use for books or writing since human intellect is gone. There is no use for weapons or medicine of any kind since there are no wars or diseases. All of this brings the Time Traveller to realize that no longer is there a need to work. "There were no shops, no workshops, no sign of importations among them. They spent all their time in playing gently, in bathing in the river, in making love in a half-playful fashion, in eating fruit and sleeping."
I am fairly sure that the answer is "knowledge." Knowledge had seemingly atrophied in Wells' time, and the promises of technology to make lives easier and more fulfilling was falling flat for many people. Therefore, if we cannot use our knowledge to build, learn, and adapt, the knowledge itself becomes rather useless, as the Time Traveler discovers.