Garrett Hardin's classic paper The Tragedy of the Commons suggests that some important problems (such as overpopulation, his main concern) have no technical solution. He's probably right, in many cases. For example, the electric cars so popular with environmental groups "release 60 times more lead per kilometer of use relative to a comparable car burning leaded gasoline" (Science 268:993).
Technical solutions do, however, have one potential advantage over those requiring "change in human values or ideas of morality." If 10% of people decide to limit their driving or the number of children they have, that will have little effect on overall pollution, fossil fuel consumption, or population growth. One might hope that the 90% would be inspired by their example, or that society as a whole would adopt Hardin's solution: "mutual coercion, mutually-agreed upon," but this is far from inevitable.
Certain technical solutions, however, do tend to spread, even in the face of significant opposition. What would happen, for example, if it became very difficult to get a surgical abortion in the US, either because of restrictive laws or because of murder and intimidation of abortion providers? The use of the abortion pill RU-486 would spread rapidly. Even if RU-486 were banned, we already have a very efficient international system for the distribution of illegal drugs. I think it's safe to assume that the black-market price for an abortion pill would be even greater than that for recreational drugs, providing an adequate motive for drug dealers to take the needed risks.
What kinds of technology tend to spread rapidly? Those that confer some advantage on the person adopting the technology. (Ideally, there will also be some advantage to society as a whole, or to the environment. Unfortunately, this is not always the case.) Advocates of "environmentally friendly" farming methods that don't actually work are always disappointed when the "stupid farmers" won't use them. But alternative farming methods that actually work (e.g., methods that reliably reduce input costs without reducing yields) are rapidly adopted. Personally, I would rather work to develop methods that increase both sustainability and profit, rather than trying to convince farmers to do something that will drive them into bankruptcy.
Here are a few ideas for technologies that I think would tend to spread (because those who would benefit from them are in a position to influence their use), which might help to solve the following problems: