Nearly all the grand challenges potentially to be faced by society as a whole in the next century have significant engineering connotations, either as part of their solution or, unfortunately, as part of their cause. That is, the Law of Unintended Consequences is alive and well.
There will, of course, be the "routine" matters, such as developing machines that better people's lives and can communicate with humans on human terms (i.e., plain language and voice); exploring Mars; establishing scheduled space tourism; solving the [living and transportation] congestion problems already confronting much of the world; and balancing the benefits of new technological accomplishments with the invasions of individual privacy that many new developments will undoubtedly generate (micro-video recorders, human implantable micro-storage devices, engineered plants and animals, etc.) In fact, some of engineering's greatest challenges may well prove to reside in the field of ethics.
There will also be the truly large challenges (my use of "large" as opposed to "grand" is, in this context, not by accident) which will likely include helping humanity recover from the destruction of several major cities by nuclear weapons at least initially employed by terrorists, and from intentionally or naturally caused pandemics in which tens of millions of people die.
The next century will, of course, see the continuation of the unfinished task of providing technologies that help society satisfy the most basic of human needs. These would include, for example, providing an adequate food supply to support the earth's burgeoning population; providing an adequate supply of clean water for all citizens of the planet (probably entailing the use of sea water); controlling and responding to major environmental shifts and weather extremes (such as would be caused by the melting of the polar ice caps) and providing a secure source of clean, affordable energy as the earth's petroleum supply wanes. Closely related is the immense challenge of assuring a life-friendly natural environment in the face of both human and naturally-caused change.
There of course remain major diseases to conquer... but more challenging is likely to be the task of enabling quality lives for individuals who routinely survive to ages far beyond those to which we have become accustomed. There is also that challenge that in part makes humans human; that is, expanding our knowledge of nature's great secrets (for example, helping scientists understand dark matter and dark energy).
Among the most immediate needs is to confront the challenge brought to us by science and engineering in the last century whereby individuals and small groups of people can, for the first time in history, produce major adverse impacts on the lives of very large groups of people; i.e., through acts of high-tech terrorism. This new asymmetry will need to be corrected and reasonable deterrents found to armed conflict at all levels (with such deterrents going well beyond classical military means, and include reducing the gap in quality of life between "haves" and "have-nots" -- by raising the living standard of all).
With respect to the engineering profession itself, perhaps its greatest challenge will be to tear down the barriers that have evolved between its various disciplines. It is likely that many of the great advances in the future will be "cross-cutting", for example, involving materials, electronics, biology and more.
And then there are, of course, the really grand challenges that could lie somewhere "out there", probably not in this century from a statistical standpoint, but nonetheless "out there". These would range from, say, the discovery of a major comet on an impact course with the earth, to a substantive communication received from a society somewhere in the universe that is a mere few hundred million years more advanced than we.
But first things first...