It's hard to imagine what the world would be like without a North or South Pole. Even if we don't think about what would happen to the poor penguins in Antarctica, Santa Claus wouldn't know where to put his workshop.

We can't think about a doomsday scenario worse than that.

Even if we had one pole, it would seriously turn things upside-down. Compasses wouldn't work at all—if they even existed in the first place. Because they measure the Earth's magnetic field to figure out where you are, losing one pole would spell the end for magnetism on earth.

Unlike with electric fields, magnetic fields don't actually have positive or negative point-charges (called monopoles) that move around attracting or repelling each other as they meet. If there were magnetic monopoles, the world would probably work similar to Alice in Wonderland, with un-birthdays, Cheshire Cats, and Red Queens everywhere.
Thankfully, we've got Gauss's Law for Magnetism to keep us from the world beyond the looking glass. According to Gauss's Law for Magnetism, there are no magnetic monopoles; there are only dipoles. Any time you find a magnetic field, it's got to have another field with the opposite charge. Having mandatory dipoles means that magnetic fields always have direction associated to them. Instead of fields of free charges just floating around, magnetic fields form loops that flow from North to South.