Ordinary ground mirages look like puddles on hot roads in the desert. They’re called inferior mirages and they’re fairly common.
Far more rare and magical are superior mirages, also known as fata morgana. They occur when a layer of very cold air is overtopped by a warm air layer. The change of densities bends the light and inverts faraway images.
Phantom icebergs, ships, mountains, or even entire cities appear upside down, floating in the air. The observed objects are often so far away that they would normally be invisible, hidden behind the curvature of the earth,
Superior mirages usually occur in polar regions over ice or cold water. Sometimes they look like spiky mountains. In Iceland these are called halgerndingar. Floating cities or ships are called hillingar in Icelandic.
In her book Half-Broke Horses, Jeannette Walls describes her grandmother’s eyewitness account of a floating town in the high desert of Arizona: “There, floating in the air above the horizon, was an upside-down town. You could see the low, flat stores, the adobe church, the horses tied to the hitching posts, and the people walking in the streets.”
Images from Astronomy Cafe
More examples at the Mirage Gallery