The noise I hate most is the sound when you catch a fish/bug/sea creature or dig up a fossil/gyroid. As soon as I get whatever it is, I turn the volume down. I hate that sound. It would be fine if it only did it for new things you got, but not every single time.
I honestly don't mind the cicadas, but I couldn't stand island beetles flying away(that's why I put the volume off when island hunting, except if I see a shark or blue marlin/Napoleonfish shadow). Plus, flying island beetles means you lost the Bells.
Where I've lived my whole life, I've heard cicadas so much that they don't bother me. I actually loved hearing them for the first time in New Leaf on July 1st (my b'day). It was like a happy b'day to me!
I hate the sound of the metronome along with any music playing in a villagers' or characters' house.
I hate the afternoon cicadas. I have a bell tree right next to my house, so the first thing I hear when I start up the game. Getting the mail, talking to villagers (villagers love standing right in front of my house and finishing right in front of my house), mail from Pete, Event notices, Resetti.
I'm more annoyed with actually finding the mole cricket than the sounds they make.