There are two important tools in which rational agents (such as you, dear reader) can be motivated externally. Reward and punishment. The carrot and the stick.
According to economic theory, agents can take rewards and punishments into account, adjust their cost benefit calculations, and change their course of actions. The first thing to take into account is that the use of both monetary and non-monetary incentives to adjust behaviour is widespread and all around us. Debates are ongoing about the efficacy of any one of them, but they are here. Different types of goods are given different VAT rates based on their merit, individuals are given salaries and bonuses, countries are given sanctions.
Although the "optimal level" of a certain reward is hard to pin down, as this is dependent on predictions, utility functions, rewards, many many variables, a more actionable question to consider in any given environment is whether rewards or punishments are most appropriate.
Punishments may be more cost-effective, given the fact that humans systematically experience loss aversion: a dollar lost feels more costly than a dollar won.
However, in several areas of life, punishments are not appropriate:
- Wages are believed to be sticky, especially downward, employees are reluctant to take a wage cut.
- Punishments may have negative lasting emotional impacts. Also in a recent funding experiments negative votes were experienced extremely negatively.
- When there is a considerable risk in the target involved. We can try to reward certain individuals if they reach a millenium prize, but marginally punishing the 99.999% of people who don't reach those goals seems counterproductive. 
However, rewards and punishments are also culturally defined. When you suggest to offer a reward where a punishment used to be in place, be ready to face controversy:
- Instead of punishing countries which do not ratify nuclear disarmament treaties, why not offer them explicit large rewards if they provide proof of nuclear disarmament? This would be a good use of international development funds.
- Instead of punishing drug users, offer them rewards if they're able to be clean.
- Instead of punishing those who failed to do something, set up a reward program. The added benefit of this is that it forces you to think about what should be rewarded and what should be punished.
The key to making either scheme work, is to have proper monitoring in place. If people are able to game your system, doing everything by or outside the rules to get access to a reward or to avoid a punishment, then you might as well throw carrots and sticks at people until they do what you want.
 Incidentally, the only person to win a Millenium Prize declined the monetary reward, showing that financial rewards are not everything. They are a powerful tool, but not universally applicable.