Actually, they do exist. There are certin times in the game that a "bad egg" could occur. But these only occur through "cheats". If you were to say, have the "One attack = kill" cheat on during a doubles match, if one of the enemy trainers runs out of pokemon, a "bad egg" may appear. It will be an "egg" named "Bad Egg". I do not know what happens if you kill it.
Now if you have a "Bad Egg" in your party, It's name will be "Bad Egg". Get to a PokeCenter, ASAP. If a "Bad Egg" Hatches, your game will crash. You will keep your last saved data, but this cane still be bad. My brother had a "Bad Egg" once, he saved and was 10 steps from a PokeCenter, but the Egg hatched in 4 steps, and with no way to get to the PokeCenter(No Fly, Dig, or Teleport), he had no choice but to restart his data.
In conclusion, "Bad Eggs" are real but don't occur other than through cheats.