Believe it or not, mosquitoes are good for more than just buzzing in your ear and giving you that itchy bump. As with all living creatures, they are a part of "the circle of life".
You see, fish eat mosquitoes when they are larvae, and birds and bats eat them when they are adult insects. Various other carnivores eat those animals, which we, in turn, eat. If mosquitoes were to be eradicated, this would throw the whole system out of order, just as if you were to do this with any living organism.
Additionally, mosquitoes are pollinators. Since the diet of mosquitoes is composed of plant nectar, they help plant life grow. You can use this to your advantage. If you live in a highly populated mosquito area, plant some flowers in your yard to attract them to the pollen, rather than your arms, legs and other delicacies.
Unfortunately, there are no more reasons that I can think of as to how mosquitoes are good. Honestly, at first glance, I write them off as one of Earth's greatest pests. However, the benefits of them that I have given should not be taken lightly. If you take mosquitoes out of the picture, you might as well take yourself out too. So before you raise your hand in the slapping position, pay a tribute to the almighty pollinator and fish/bird/bat food.