In short, the world would cease to function as we know it without the animals we call "bugs." Insects, spiders, and the like represent perhaps half of all known species and, in many places, most of the animal biomass. They are the primary and often the secondary consumers in most terrestrial food webs. They are essential for pollinating flowers and breaking down dead plants and animals. Without them, there would be very few other living things in our world. It's been said that insects are the "little things that run the world."
Remember, every creature plays an essential role in its natural environment and removing it weakens the entire system.