The largest nuclear bomb ever detonated was the Tsar Bomba (Russian "King of Bombs"). The mushroom cloud reach over 35 miles in height. Total destruction out to a radius of 22 miles. Various levels of damage were detected out to a radius of over 550 miles. It was detonated over Novaya Zemlya (the sickle-shaped island north of Russia) and it broke window panes in Norway and Finland! It vaporized a glacier! The initial fireball was 2.5 miles in diameter and was hotter than the sun. Tsar Bomba had an estimated yield of 57 megatons. That's more than 3500 times the strength of the bomb we dropped on Hiroshima.
0.9 miles away from the hypercenter is completely vaporized. 1.1 miles away from the hypercenter, some debris and rubble can be found. 1.5 miles away from hypercenter, heavy damage to reinforced buildings. 2.2 miles away from hypercenter, moderate damage to reinforced buildings. 3.6 miles away from hypercenter, any remaining buildings are on fire. 7.5 miles away from hypercenter, buildings destroyed from air blast. 15.0 miles away from hypercenter, some extent of damage to buildings and survivors are unlikely. 20.5 miles away from hypercenter, damage likely and survivors likely. 24.5 miles from hypercenter, damage from flying debris and only affected by gamma radiation emitted by explosion.
The largest bomb exploded was the USSR Tsar Bomb in 1961. At 57 megatons, it's the largest ever tested. It's design was for 100 megatons, in three stages, but the explosion would have been so large as to destroy the drop plane. Because of its design, 97 percent of its yield is due to fusion, making it the least-radioactive bomb to be exploded, when yield is considered. The plane piloted by Andrei Durnovtsev dropped the Tsar Bomba at 11:32 AM Moscow time, from a height of 6.5 miles (10.5 km) over Mityushikha Bay in Novaya Zemlya. The bomb detonated at a height of 2.5 miles (4 km). The descent from the height it was dropped from until the place of the detonation at 4,000 meters above ground took 188 seconds, just enough time for the pilot, Andrei Durnovtsev to fly to a safe distance. Just one second after the detonation, the fireball was already 4 miles wide, and the light could be seen at distances of over 2,000 kilometers. The mushroom raised to a height of about 64 km, over 7 times the height of Mount Everest. The blast melted rocks in ground zero, and total destruction extended to a radius of 40 miles; extensive damage observed at 50 miles. Curiously, this was only one-quarter of the energy expended in the Krakatoa eruption of 1883.
Modern ICBMs (land- or sea-based) have yields between .1 and .4 megatons (Mt). Bombers carry dial-a-yield weapons typically 10 times more powerful. Typical complete destruction radii are orders of magnitude less than that of the Tsar Bomb test. This is because the MiRV design coupled with incredible accuracy means smaller yields are necessary to achieve the desired result.