Left wing individuals and think tanks (like the Economic Policy Institute) continuously argue that real wages have not kept up with increasing productivity. This is typically followed by claims that the government needs to tax the rich more, or we need more labor unions, a higher minimum wage, etc. However, as usual, the claims made by the left typically are either disingenuous, or based on ignorance, and the claim that worker’s wages have stagnated is no different.
First of all, how are wages and productivity related? Economic theory predicts that worker's compensation is based on their marginal productivity. This theory is called the Marginal revenue product theory of wages. According to wikipedia, the "marginal revenue product of labor, is the change in total revenue earned by a firm that results from employing one more unit of labor." In competitive labor markets, neoclassical theory predicts that a worker's wages will be equal to the marginal revenue product that, that worker brings to the firm employing him. This is because if firms do not pay workers according to what their labor is worth (the more productive, the higher the wage), other firms have an opportunity to profit by enticing that worker to work for them at a higher wage. It's sort of like biding on a dollar. If one person bids $0.90 on a dollar, another person will bid $0.91 because there is an opportunity to profit from doing so. This bidding war will continue until there is no longer an opportunity to profit from doing so. However, has economic theory been debunked by the fact that wages and productivity have not grown together?
It's important to note that wages are not the only form of worker compensation. Today, a large share of worker compensation is in the form of health benefits, pensions, etc. When we take these into account, it is clear that total worker compensation has in fact risen 30% since the 1970's, when adjusted for inflation using the consumer price index.
But there is still a large gap between worker compensation and productivity. How can this be explained? Well, this is mainly due to the fact that economists measure average productivity for inflation using an index known as the implicit price deflator. When left wing thinks tanks like the Economic Policy Institute measured worker's wages for inflation, they did it with the consumer price index (also the above chart measures worker compensation using the CPI). Comparing the relationship between average worker compensation and average productivity, while using different price indexes is comparing apples to oranges. Martin Fieldstein, the former President of the National Bureau of Economic Research has written:
"Although any consistent deflation of the two series of nominal values [avg productivty vs. avg worker compensation] will show similar movements of productivity and compensation, it is misleading in this context to use two different deflators, one for measuring productivity and the other for measuring real compensation...when we recognize the multiproduct nature of the economy, we say that the competitive firm pays a nominal wage equal to the marginal revenue product of labor, i.e., to the marginal product of labor multiplied by the price of the firm’s product. The key real relation must therefore be between changes in productivity in the nonfarm business sector and changes in the nominal compensation paid in that sector deflated by the product price and not by some consumer price that also reflects goods and services produced outside the domestic nonfarm business sector." 
In short, the consumer price index measures inflation for certain consumer products. However, worker's don't just produce consumer products, they also produce goods and services which are bought by businesses and are thus not represented in the consumer price index.To accurately compare average worker compensation and average productivity, one must measure inflation for each of them using the IPD. When this is done, Fieldstein finds:
"the doubling of productivity since 1970 represented a 1.9 percent annual rate of increase. Real compensation per hour rose at 1.7 percent per year -- when nominal compensation is deflated using the same non-farm business sector output price index. In the more recent period between 2000 and 2007, productivity rose at a much more rapid 2.9 percent a year and compensation per hour rose nearly as fast, at 2.5 percent a year." 
As you can see, when average worker compensation is measured for inflation using the same deflator as average productivity, the gap between them is very small. Even then, Fieldstein writes:
"Changes in productivity are not immediately reflected in compensation. The concurrent (within year) effect of a rise in productivity is less than a one-for-one rise in compensation." 
Thus, there is a lag between an increase in productivity and an increase in worker compensation. According to his calculations, the within year effect of a rise of $1 of productivity will lead to a rise of $0.79 of worker compensation. However, after two lagged changes in productivity are measured, worker compensation rises $0.94 for every $1 increase in productivity. 
Fieldstein says that the reasons for these lags must be examined further, but concludes saying, "basic theory reminds us that real compensation should be measured using the same price index that is used to calculate productivity. When this is done, the rise in compensation has been very similar to the rise in productivity" .
It is also worth noting that, "Total employee compensation was 66 percent of national income in 1970 and 64 percent in 2006. This measure of the labor compensation share has been remarkably stable since the 1970s. It rose from an average of 62 percent in the 1960s to 66 percent in the 1970s and 1980s, and then declined to 65 percent in the 1990s where it has remained from 2000 until the end of 2007."  Thus, there doesn't seem to be much evidence that workers are not benefiting from increased productivity and there is a tremendous amount of evidence that they are.
 All graphs taken from here: http://www.heritage.org/research/reports/2013/07/productivity-and-compensation-growing-together#_ftn2