Why do many humans have bad eyesight, such as near-sightedness, which hampers performance in a wide variety of tasks? Shouldn't there be evolutionary pressure towards better eyesight?
Remi.b and Potterbond007 have put forward excellent answers. Would like to add something..
One of the reasons that Myopia (near sightedness) happens is because of use of eye in work like reading, which requires working with close objects. I don't think there was much working with close objects in the past. So very few people with myopia might have been present (and of course, they may have had disadvantages in catching prey.)
Other common disease is hypermetropia which generally occurs during old age, past the reproductive prime, so it could not have much evolutionary impact.
With nearly 40,000 years of natural selection on eyesight, prior to the invention of eye glasses, there needs to be a better explanation than the effects of 'modern' technology. There are two likely reasons for the persistence of "poor" eyesight in humans. First, humans are social animals and live in groups. Within groups there is frequently a division of labor. This division of labor deemphasized the importance of vision. Individuals with "poor" eyesight could easily maintain a high fitness (reproductive success) in this social structure. Second, humans have long term parental care (both within and among families - again a function of social living). Most human offspring maintain close familial connections up to and including the age of reproduction. The strength of selection on eyesight diminishes past reproductive age, allowing individual with poor eyesight to have relatively high fitness.
Maintenance of Polymorphism and Mutation Load
There are many possible reasons why some amount of deleterious alleles are maintained in the population. One of which is the mutation-selection-drift balance. In short: Because mutations always occur, there is continually an input of deleterious mutations in populations genome resulting in some fitness decay (called mutation load). While mutations create this polymorphism, processes of selection and genetic drift cause a decrease in polymorphism. At equilibrium there is a balance between mutations, selection and drift called the mutation-selection-drift balance. You may also want to consider various population structure related concepts such as migration between patches. Haldane first explored this mutation load theoretically and estimated that the fitness of an existing individual in a population of perfect (deleteterious-mutations-free) individual is about 80% lower, which is huge! Such mechanism can explain various disease found in a population.
Age-specific intensity of selection
Also, for the question of disease appearing late in life (which is often the case of eyesight related disease), it is important to realize that those genes which are expressed late in life undergoes a lower selection resulting in a higher mutation-selection-drift balance. See this post for more info.
Impact of Medicine and social helping on the intensity of selection
As pointed out by @potterbond007 modern medicine allows to diminish the deleterious effect of some mutations. For example, one that has clubfoot may be operated and is likely to survive and reproduce and therefore propagating its deleterious alleles. This would be different in some past. Therefore, medicine diminish the selection pressure on deleterious alleles. However, modern medicine probably has a very low effect on our genomes because it is so modern. 100 years ago we could not operate clubfoot and 500 years ago (almost) nobody had glasses to correct for eyesight deficiency. We may go a bit further in the past and also consider that social interactions such as helping weak individuals in a tribe may also have decreases the selection pressure against deleterious alleles (more info in @theBIOguy 's answer). Of course, if selection is diminished the mutation-selcetion-drift balance is increased and deleterious alleles are more common and mutation load is greater.
Further investigations will be needed in Epidemiology
Assuming that eyesights disease are particularly common and deleterious, we should have a closer look to the epidemiology of the diseases of interests. If it seems to you that eyesight-related diseases are more common and more important in terms of their effects on fitness than diseases on other traits then, you may want to seek into some physiological and developmental explanations that may tell you why eyes are so likely to be impacted by genetic and/or environmental factors. I personally have absolutely no knowledge about the epidemiology and developmental mechanisms of any eyesight disease! Also considerations of the impact of modern environment should be considered such as the impact of TV and computer screens on our eyes (more info in @biogirl 's answer)
Mainly because we haven't been forced to remove the bad genes that cause these defects from our gene pool. In ancient times, a bad gene that causes poor eyesight would have made it difficult for a person to spot prey or escape from a predator. However, we have glasses now which gives the bad eyesight gene as much a chance to propagate as any other gene. it also doesn't really matter since poor eyesight is never a factor for survival in present times. The same with poor hearing which we correct with hearing aid. Please read this for an article in the guardian and this article in the orlando sentinel. You could also read this discussion on reddit to see a few fun arguments.