The 1--2 September 1859 magnetic storm was the most intense in recorded history on the basis of previously reported ground observations and on newly reduced ground-based magnetic field data. Using empirical results on the interplanetary magnetic field strengths of magnetic clouds versus velocities, we show that the 1 September 1859 Carrington solar flare most likely had an associated intense magnetic cloud ejection which led to a storm on Earth of DST ~ -1760 nT. This is consistent with the Colaba, India local noon magnetic response of ΔH = 1600 ¿ 10 nT. It is found that both the 1--2 September 1859 solar flare energy and the associated coronal mass ejection speed were extremely high but not unique. Other events with more intense properties have been detected; thus a storm of this or even greater intensity may occur again. Because the data for the high-energy tails of solar flares and magnetic storms are extremely sparse, the tail distributions and therefore the probabilities of occurrence cannot be assigned with any reasonable accuracy. A further complication is a lack of knowledge of the saturation mechanisms of flares and magnetic storms. These topics are discussed in some detail.