Bees are probably the most important creature on Earth, in my opinion. They pollinate so many plants that most terrestrial organisms depend on. Our entire ecosystem relies on plants, and those plants rely on bees. Bees also give us honey and wax, but that isn't nearly as important as their effect as pollinators.
Maggots are immature flies that are used in medicinal therapy to remove decaying tissue from non-healing wounds.
Many insects are a food source for humans, although not really popular in the Western world.
As you see in crime dramas, fly pupation really can indicate time of death of an individual and is very specific, depending on temperature.
Insects that clean up decaying matter like leaves and dead animals keep those leaves and dead animals from piling up and rotting.
Insects are AWESOME biological control agents. Aphids are pests that ladybugs happen to love, so having them around naturally controls the population and saves your rose bushes.
This is probably not what you're looking for, but they also make great fishing bait. :)
Insects are super cool and help humans in many direct and indirect ways!
College insect ecology course