Since Yaga49 typically asks questions about economics, let me approach this from an economic point of view.
First, we must be clear on what we are talking about. Wage discrimination only exists if women are paid less for doing the same job at the same level of quality and productivity as men. It does not exist simply because women, on average, make less money than men. This sort of wage discrimination will, according to economic theory, have to end.
The reason for this is that firms that engage in wage discrimination should be less competitive than those that do not. Women will not want to work for discriminatory firms. Therefore, those firms will be unable to attract talented women. This will cause them to be less competitive than firms that can draw from the most talented men and the most talented women. According to economic theory, then, wage discrimination cannot last long because it is not beneficial to firms to engage in such practices. It may persist to some degree since it is not easy for people to find out which firms do and do not discriminate, but it should become very rare.
If we are talking about simple disparities in wages (women being paid less than men in general), this is something that is less likely to disappear soon. This sort of disparity comes largely from noneconomic factors. For example, women earn less than men in some sectors because women with children are sometimes less able to put in the kinds of long hours that men put in and therefore are passed over for promotion. This comes about because women are still expected to bear most of the burden of raising children. This sort of thing may decline over time, but there are not many economic forces that can cause it to do so.
Thus, literal wage discrimination should disappear, but wage disparities might not disappear so quickly.
This is an important question.
On the one hand, wage discrimination based on gender still exists and it is well documented. However, there seems to be progress. In light of this, I believe that at one time in the future, this discrimination will end for three reasons.
First, women are becoming more powerful in the world. We could have had a woman president. And other nations that are more male centered than America now have women presidents, like South Korea.
Second, more people are talking about this topic. This means that the injustices of this will become more apparent. When this does, the practice will decline.
Finally, people are now more educated and hopefully more enlightened. This, too, will help the issue at hand, as there is no way a woman should make less than a man, as long as they are both qualified.