Trade cannot disappear, because it is essential for civilized life. Man is born naked and helpless, and in order to thrive he needs nurturing, education, shelter, food, clothes, and so on. In order to satisfy his needs, man trades goods and services for other goods and services. Even some animals do it. There is no way to do away with trade without reducing man to the life of a mindless beast.
Money was invented in order to facilitate trade. Without money, trade takes by necessity the form of barter, where goods and services are exchanged directly for other goods and services. (See this answer for a more detailed account.) Money was used since ancient times as a universally accepted medium of exchange, in order to eliminate the complexities of barter.
In the future this may not necessarily be necessary anymore.
Marvin Minsky, one of the legendary figures in Artificial Intelligence research, hypothesized that with the development of IT, there may come a future when
With fast computers and huge memories, we could have a nonlinear database that would better understand what each person has and wants. Then, by using complicated game theory-related computations, it might turn out that in general everyone would get more (in terms of their personal values) for the goods that they are willing to “sell”.
(See for example here and here.)
He was quick to add that
I don't think anyone will care that much--at least in the distant future, because once the intelligent robots come, we could all be as wealthy as kings.