When the player shakes trees, bees may appear. They are hard to catch. In Animal Crossing, they sell for 4,500 Bells, but in City Folk, they sell for 2,500. They can sting the player, which causes their right eye to swell up. Villagers will react to this. You can get rid of the sting by buying medicine (Animal Forest E+, Wild World, and City Folk only), or, in all versions, by saving and quitting, then logging back on in your file.
They were brought back to New Horizons as wasps. You can buy medicine from Nook's Cranny to deal with the stings.