Any explosion above a pretty small scale is likely to result in a mushroom cloud. An explosion occurs when a dense substance, usually solid or liquid, turns into a gas. The result is an enormous and fast increase in its volume, or size. Most explosions we are familiar with involve the production of heat. An atomic explosion is no exception. The hot gas, being less dense than the air around it, rises.
As the gas rises, it also continues to expand. The expansion and contact with cool air above the rising column causes the gas to cool. Hot gas from below is still trying to rise, and the cooling gas above it is in the way. This makes the cloud of smoke and dust spread out like the head of a mushroom. This structure is a vortex, like a smoke ring (Do people even make smoke rings any more?) with a torus, or doughnut, shape, the gas on the inside traveling up, out across the top, down the sides, and back up through the center.
Volcanoes can make mushroom clouds if they explode with enough force. The volcanic explosions that formed the Valles Caldera behind Los Alamos must have made spectacular mushroom clouds! According to Wikipedia, the largest mushroom clouds ever seen were on Jupiter during the impacts of Comet Shoemaker-Levy.
