The first planetary magnetic field investigated, and the biggest one by far, was that of Jupiter. In early 1955, two young radio-astronomers started working with a cross-shaped antenna array of the Carnegie Institution's Department of Terrestrial Magnetism (DTM). The array could select signals from a narrow range of directions, and Ken Franklin and Bernie Burke calibrated it using a known source, the Crab Nebula, then began surveying the surrounding sky.
They found another conspicuous radio source [Franklin, 1959], but unlike the Crab, its position shifted as days passed. Standing next to the array one night, Bernie noted a star overhead and asked Ken "what is that bright thing up there?" It was Jupiter, and that was where the signal was coming from. In publishing their result, the astronomers speculated "the cause of this radiation is not known but is likely to be due to electrical disturbances in Jupiter's atmosphere."
In 1959, when the Earth's radiation belts were already known, Frank Drake observed Jupiter's emissions and concluded from the relative intensities in a range of wavelengths that their radio waves were probably produced by electrons trapped in a strong magnetic field. Then in 1973 the space probe Pioneer 10 passed by Jupiter and found there, sure enough, an enormous planetary magnetic field and a very intense radiation belt.
The strength of the source of Jupiter's dipole field--its dipole moment--is some 20,000 times that of Earth. Like the Earth's dipole, its axis is inclined by about 10° to the rotation axis, but its polarity is in the opposite direction of the Earth's (until the next reversal, at least). What produces that field is still unclear. Jupiter's core may well consist of hydrogen, compressed by the huge weight of the planet's outer layers to where it becomes a metal and conducts electricity [Nellis, 2000]. The strange radio signals observed by Franklin and Burke came from Jupiter's radiation belt, the most intense one in the solar system--so intense that after just one pass through it, Pioneer 10 suffered some (minor) radiation damage. Along with its radiation belt, Jupiter also has intense auroras, observed from Earth and from orbiting telescopes.
The Jovian magnetosphere is very different from the Earth's. It is much bigger, extending to 50-100 RJ (Jupiter radii; 1 RJ is about 10 RE), and unlike the Earth's, its plasma seems to co-rotate with the planet up to the dayside boundary with the solar wind. It contains not just protons and electrons, but also ions of sulfur and sodium, probably emitted from the moon Io (see below) and it carries a very extensive ring current. That current is concentrated near the equator, creating a magnetosphere much more flattened than Earth's, so much that it has been referred to as the Jovian "magnetodisc."
Jupiter's magnetic field has some interesting interactions with the planet's larger moons, which are bigger than ours and whose absorption creates distinct dips in the radial distribution of plasma. Io, the innermost large moon, is a bizarre world heated internally by its tides, with active volcanoes and a thin atmosphere. Its ionosphere and/or body conduct electricity, and the relative motion between it and Jupiter's magnetosphere creates a dynamo circuit, producing currents of a few million amperes which flow between Io and Jupiter's ionosphere.
This remarkable phenomenon was anticipated by Goldreich and Lynden-Bell  and by Piddington and Drake  who suggested it as an explanation for the curious effect of Io's position in its orbit on decameter wave radio emissions from Jupiter's magnetosphere. The theory of Goldreich and Lynden-Bell was finally confirmed in 1993 by the observation of infra-red emission from the footpoints in Jupiter's ionosphere of the "Io flux tube," of field lines which threaded Io [Connerney et al., 1993] . The space probe Voyager 1 passed close to the Io flux tube on March 5, 1979, and observed the magnetic field of its currents [Acuña et al., 1981].
All four giant planets--Jupiter, Saturn, Uranus and Neptune--were visited by Voyager 2. (The first two were also visited by Pioneers 10 and 11 and by Voyager 1, and the probe Ulysses flew by Jupiter, while the probe Galileo is currently in orbit around it.) In all four the dipole moment--the strength of the bar magnet which, if placed at the center, gave a comparable field--was much greater than that of the Earth (see Table 2, above).
Voyager 2 unexpectedly found the magnetic axes of Uranus and Neptune to be inclined by about 60° and 45° (respectively) to their rotation axes. The shape and properties of a planetary magnetosphere depends on the angle between the flow of the solar wind (i.e. the direction from the Sun) and the magnetic axis, and for those two planets, that angle varies rapidly as the planet rotates. As a result, their magnetospheres undergo wild variations during each rotation, although each manages to contain some trapped particles. The origin of all those fields is unknown. Saturn is big enough to produce metallic hydrogen in its core, and interestingly, its magnetic and rotational axes are the same within observational accuracy. The magnetic fields of Uranus and Neptune might be generated in relatively poorly conducting "icy" interiors, perhaps explaining their large dipole tilt and complex field geometry.
The planet Venus was visited by Mariner 10 in 1974, which continued from there to Mercury. Venus was found to be unmagnetized: the solar wind is only stopped by its upper atmosphere, the Venus ionosphere, creating a completely different type of magnetosphere, more like a comet tail. On the other hand, tiny Mercury--an airless rock only moderately bigger than our Moon, rotating very slowly--surprised observers by being magnetized. Its magnetic field is weak and probably does not extend far enough to trap many particles, but as the spacecraft passed through its nightside tail, it observed a sudden spasm in which particles were apparently energized. NASA has scheduled the Messenger mission to fly to Mercury and orbit it, and the European Space Agency (ESA) is planning a Mercury mission as well.
Mars [Acuña et al., 1999] and the Moon [Fuller, 1974] have permanently magnetized patches of rock on their surfaces, suggesting that even if they now lack a dynamo field, at some time in the past they might have possessed one. That would agree with the giant volcanoes (apparently extinct) observed on Mars, which suggest a hot interior, although the volcanoes themselves are not associated with magnetic patches. On Mars, in particular, these patches (as observed by the Mars Global Surveyor) create fields about 20 times stronger than the surface magnetization of Earth (as distinct from the Earth's core magnetic field) would create at the same distance of observation.
Planetary magnetic fields thus seem to be the rule, not the exception, at least in our solar system, though the origin of those fields may be quite different from that of ours. Researchers who feel frustrated by their inability to conduct direct observations on the Earth's core should note that the source regions of those fields are even less accessible. Thus, as the study of planetary magnetic field enters its second millennium, it faces more unanswered riddles than ever before.
Often in a field of science the lode of research seems to run out, as major problems are resolved and attention turns increasingly to details. Geomagnetism shows how disciplines may rejuvenate themselves by shifting their focus to new targets and new methods.
Geomagnetism started with the mapping and monitoring of the global magnetic field. Then in the early 1800s a new class of phenomena entered the picture, magnetism caused by electric currents. Work by Faraday in that direction, together with astronomical studies of sunspots, led by 1919 to the notion of the self-exciting dynamo. Though this seemed like a promising way of explaining the Earth's internal field and its time variations, nearly another century passed before modern computers allowed the terrestrial dynamo to be even approximately modeled. Meanwhile the observation of rock magnetism suggested the occurrence of magnetic reversals, and dynamo theory turned out to be consistent with reversals, too. In the 1960s these observations combined with Wegener's ideas of moving continents and with studies of mid-ocean ridges, to produce the science of plate tectonics,. Magnetic storms (first observed in the 1700s) and related "northern lights" remained a mystery until after 1958, when artificial satellites started probing the Earth's distant magnetic field. And finally, planetary magnetic fields observed by distant space probes suggest that several different processes of planetary magnetization may exist.
All these changes helped geomagnetism stay in the forefront of geophysics, in one form or another. One is reminded of the Japanese board game of Go, where two opponents using black and white counters take turns placing them on the intersections of a board ruled in squares, each trying to surround and "choke" pieces of the opponent. A player's "soldiers" survive only as long as they have access to some unoccupied "breathing space." Disciplines of science are like that, too: they only "live" as long as they touch some unsolved areas, as long as they can lay claim to yet-unsolved mysteries. It has been the good fortune of geomagnetism to succeed in doing so over four centuries. The past never guarantees the future, but it is to be hoped that the field still has a long way to go.
Acknowledgment The author thanks the many colleagues whose comments helped shape and improve this article, in particular, David Barraclough, Stuart Malin, Jack Connerney, Henry Frankel and Raymond Hide.