This section contains a summary of Babylon 5's story arc (the 5-year plotline) up to, but not including, "Babylon Squared." Note that this is chock full of spoilers!
The pilot, "The Gathering," was set in the year 2257; Babylon 5 had recently come online. The last of the ambassadors, Kosh, arrived on the station, prompting an assassination attempt. Sinclair was framed for the attempt, but was eventually cleared when the real culprit -- a Minbari -- was discovered. Many mysteries were introduced: Sinclair's missing 24 hours on the Battle of the Line (with the announcement by the Minbari that "there is a hole in your mind"); the mystery of Kosh, seen only by the doctor and the telepath; and the disappearance or destruction of the previous four Babylon stations.
Season One began with "Midnight on the Firing Line," about 6 months later. Lt. Cmdr Susan Ivanova replaced Lt. Cmdr. Takashima as second-in-command; her dislike of the Psi Corps became evident when Talia Winters arrived. A Centauri agricultural outpost was attacked without provocation by the Narns. (In broad strokes, this episode portrayed the Narns as the "bad guys" and the Centauri as comic relief.) Luis Santiago was reelected President of the Earth Alliance.
A "Soul Hunter," a member of an order which collects and preserves important souls, found himself on the station, and attempted to collect Delenn's soul prematurely. The Minbari, it was revealed, greatly value souls; they prevented a soul hunter from taking the soul of their great leader Dukhat, so that his soul would be reborn into the next generation. Delenn was called Satai by the soul hunter, which prompted Sinclair to wonder if something was going on, as Satai is the title used my members of the Grey Council, the Minbari ruling body and highest religious authority.
In "Mind War," two Psi Cops -- P12 level telepaths, including Bester (played by Walter Koenig) -- came to the station in search of telepath Jason Ironheart, who had achieved telekinetic abilities and was transforming into something more than human. Ironheart warned Sinclair that the Psi Corps is starting to pull the strings in the government back on Earth. When Bester's partner was killed, Sinclair made a new enemy. Before departing, Ironheart gave Talia a gift: telekinesis, and maybe other abilities as well.
"The War Prayer" introduced members of the Homeguard, an anti-alien organization back on Earth.
"And The Sky Full of Stars" explored what happened to Sinclair on the Battle of the Line, 10 years before in the Earth-Minbari War. Interrogated and forced to relive the battle, we saw Sinclair ram a Minbari Cruiser, only to wake up on board, interrogated by the Grey Council. He recognizes Delenn as one of the Grey Council. After escaping from his interrogators, he chose not to reveal to Delenn that he remembered part of his missing 24 hours.
"Deathwalker" was a notorious war criminal from the Dilgar War, fought by Earth and others several decades earlier. She had a substance she claimed granted immortality -- but only at the cost of another's life. The Vorlons destroyed her ship to prevent Earth from gaining the secret of immortality.
"Survivors" pulled Garibaldi back into his alcoholism amid accusations of sabotage. The real culprit was the Homeguard.
"Signs and Portents" deals with an attack by raiders on the station. The B-story, in which Londo acquired the long-lost symbol of his empire, the Eye, was more important. A mysterious, polite man named Morden inquired, "What do you want?" of the alien ambassadors, and seemed to like Londo's response -- for the Centauri to reclaim their lost empire -- the best. The Eye was captured by the raiders, who were destroyed by a mysterious ship that appeared out of the shadows. Morden returned the Eye to Londo, "from friends you don't know you have."
In the two-parter, "A Voice in the Wilderness," it was discovered that the planet below B5 is not as dead as was thought. The Mars colony broke out in rebellion. A dying alien was found controlling vast, tremendously powerful machinery on the planet below. Draal, an old friend of Delenn's, took charge of the machinery in the planet, warning away all who would try to take it for themselves. The Mars rebellion was put down by Earth Alliance security forces.