What would happen if flies became extinct?
It's not as hypothetical or silly a question as some of the other answers seem to presume. Humans are close to having sufficient command of genetic technology to erase a species from the Earth. We will do this for species that are sufficiently annoying. Mosquitoes? On notice. Right now the environmental scientists think they are winning that argument, but I figure it's cause the "death to mosquitoes" camp is biding its time. No need to get aggressive when the technology to do it is not entirely solid (and might accidentally kill lots of things, like things related to the target mosquitoes)
Speaking of killing lots of things, imagine if we accidentally wiped the flies. If we accidentally wiped out all flies, we'd be choking in dead, rotting carcasses. Not just the creatures that would have been cleaned up, but all the things that needed flying insects to be around in order to live, and then all the things that depended on those things and up the food chain. Kill off the mosquitoes that carry specifically malaria and other nasties? Certainly quite a bit of environmental damage, but other mosquitoes could step up and there's plenty of flying food for the birds and bats. Kill too broadly, and the result is absolutely terrible.
Which, in a nutshell, is why we banned DDT. DDT is entirely harmless to humans and destroys pests we hate. But it kills too broadly, and we had to step back from the brink of doing irreparable harm to our ecosystem (which even if you don't care about "ecosystem" I can replace that with the words "functioning farms" and pretty much everyone is in favor of those.)
If by "flies" you mean entire order Diptera, than it would be almost impossible. It would take bigger catastrophe than meteor impact that killed dinosaurs 65 millions years ago. Such event would likely wipe off all multicellular life from the planet.
But if such extinction would be a slow process, than other life forms would try to take place previously occupied by flies, other species that were dependent on flies would either adept to new environment or face extinction .
But to be honest, even the best scientists wouldn't be able to properly predict such complicated scenario.
A partial answer includes a lingering stench of rotting animal carcasses, which fly larvae use for food as they develop; the earth is cleaner as a result. Even dung is useful to dung beetles. Flies are important food sources for other insects, e.g., dragonflies, and for many species of birds, and fish will eat flies with gusto, too. Birds - chickens, quail, grouse, etc. - love to eat fly larvae (maggots). S o many other organisms would suffer if flies (houseflies) became extinct.
I would be happy, I hate the pesky things.
I suppose fishermen would be a bit peeved.
Maggots are the bait for the fish.
Hey, what do you call a fly with no wings?