The Spacing Guild has an ability monopoly on interstellar travel: with the use of melange, guild navigators are the only beings capable of piloting the massive Guild Heighliners safely through space. The heightened awareness and prescience the spice grants allows the navigator to plot a safe course between the stars, and to then 'fold' space, allowing a nearly instantaneous trip.
The guild is apolitical (with exceptions, noted below), since their monopoly allows them to dictate terms to all parties that preserves the economy that supports them. As the only party able to transport goods in an interstellar economy, the Guild's highest concern is that commerce continue; for commerce to continue, the Guild must continue; for the Guild to continue, melange must be available. Ultimately, the Guild's only concern is that melange continue to be mined on Arrakis.
Thus, the Guild holds veto power over all wars and political maneuvering. Military action is permitted, as long as the Guild is paid high rates to transport the troops, but major upsets in the political order of the universe must be approved by the Guild. In Dune, Paul Atreides defeats the Emperor Shaddam IV in a battle on Arrakis, and demands first the emperor's daughter for a wife, which would make Paul heir to the throne, and second that the Emperor immediately step down in favour of his heir. The demands are coupled with a threat to destroy the spice. Since that would end all interstellar transit, the Guild sides with Paul, threatening to strand the Emperor and his troops on Arrakis if he doesn't accede.
Guild navigators are human, at the beginning; but their constant exposure to high levels of spice mutates them. Since melange is addictive, with death the unavoidable consequence of withdrawal, navigators make a one-way trip into their profession, spending their whole lives in a mobile tank in which they are constantly immersed in a cloud of spice. Navigators are made prescient by the spice (a requirement of being a pilot), and are sometimes utilized as such: In Dune Messiah, a navigator named Edric takes part in a plot to assassinate the emperor, Paul Atreides. The presence of a prescient hides the activities of that person, and those around him, from other prescients; Edric's involvement is solely to protect the conspirators from Paul's prescient sight.
In the fifth and sixth novels of the series, Heretics of Dune and Chapterhouse Dune, which occur 8,500 years after the reign of Paul Atreides, the technocrats of Ix have developed a replacement for the Guild navigators, a technological solution that obviates the need for prescience to safely guide interstellar spaceships. Furthermore, the prescient rule of Leto II that lasted 3,500 years has shown the universe the perils of prescience, namely that the entire universe can be locked into the vision of a single entity, giving that entity absolute power. The Guild, facing obsolescence and suspicion, couples itself with Ix in decline; Guild navigators continue to exist, but their importance in the universe is severly diminished.