Because scientific breakthroughs can’t really be predicted and because of the limitations of gravity and wind drag, aircraft of the future aren’t expected to fly much faster than they do now; at least not the kind that flies in the atmosphere.
While it’s true that lighter metals and composites will likely be discovered, especially as nanotechnology develops, the effect is more likely to be better gas mileage which hopefully would translate into lower ticket prices for commercial airlines.
Also, because of the failure of the Concorde (SST) to catch on, commercial airlines will likely continue to be wary of any new aircraft whose merits are based more on speed than cost reduction.
Having said that though, there is the possibility that new engines that are being developed and tested by several countries might provide the breakthrough that is needed to finally bring trans-continental travel times down to a more reasonable level. The United States for example, recently tested a brand new kind of engine (scramjet) that was mounted on an unmanned plane that broke speed records for a military fighter jet configuration and estimates are that it might increase possible aircraft speeds tenfold as design issues are figured out.
The dream of those that run commercial airlines however is a new type of fuel that is not only cheaper but has a more stable price. The new pilotless jet that was flown, though top secret, was reported to be flown using conventional jet fuel, but in a nonconventional way which might mean increased mileage and shorter flight times. But other future possibilities might include hydrogen or even nuclear power. It might be noted that nuclear submarines regularly cruise the oceans depths without need for refueling for decades.
There is also the possibility that long distance flights will fly much higher, which would allow them to fly faster without using more fuel. The reason this looks possible is because of the commercial propositions that are now able to make ventures into space without the aid of government assistance.
Another factor that is likely to spur new technological developments in aviation is the rise of new competition. For most of the history of aircraft, the United States has dominated the engineering, construction and sale of commercial and many types of military aircraft. As China, India, Brazil and other nations grow in prowess though, there is likely to more innovation, and hopefully new discoveries that could lead to getting from one place to another faster, cheaper, and safer than that which we now enjoy.