In one episode, a plaintiff in a courtroom is suing one of The Greys because his ancestor was abducted by the alien's ancestor, a Shout-Out to the modern day abductee phenomenon.
Word of God is that the Canticle reference was not intentional. He had been doing research on monasteries for another project, and so had them in mind when he was writing the episode. It wasn't until later that he realized he'd pretty much done A Canticle for Leibowitz, but he couldn't think of another way to do the scene that worked as well, so he kept it as is.
Lampshaded in the RPG. According to John Carter, it was a coincidence.
Any episode taking place on Mars is reasonably likely to feature some reference to Mars-based sci-fi, oftentimes in the forms of street names, business names, or background artwork. Admit it, if we colonized the planet in Real Life, that'd be hard to resist doing anyways.
In his notes about the first Psi Cop episode, Mind War in the collected scripts, JMS notes that Bester has no first name in this appearance (he's just "Mr. Bester") and that he originally didn't intend to use Alfred as he was a Batman fan and couldn't imagine a villain named Alfred, but the name got used in ancillary materials and he went with it. Considering that Psi Corps is basically a Darker and Edgier version of The Demolished Man it seems fair. In the Psi Corps novels, it becomes an in-universe shout out as the author Bester existed in the B5 universe and telepath Bester's grandfather renames him after the writer.
Speaking of Bester, the character used Isaac Asimov 's Laws of Robotics from 'I, Robot' when he re-programmed Garibaldi to track down the conspiracy control telepaths via a virus, to ensure Garibaldi couldn't take revenge.
Multiple Shout Outs to George Orwell's 1984: Ministry of Peace, rewriting the dictionaries, etc.
The punishment given in lieu of the death penalty, the Death of Personality, is also a Shout-Out to The Demolished Man, where the process of telepathically wiping a criminal's personality is called Demolition.
Much of the philosophy spouted by various races is only slightly re-worded from human thinkers. For instance, much of Minbari philosophy is a reworking of things Carl Sagan said. His "Star Stuff" speech from the Cosmos special is repeated almost verbatim by Delenn in the pilot. Given that modern Minbari philosophy and religion was essentially created en masse by a time-traveling Sinclair in his guise as Valen, it may be that Sinclair directly cribbed from Sagan.
JMS was very touchy on the subject of Shout Outs. He stated that freelance writers got carried away with them in the first season, and he put a halt on them after that. He also claimed that much of what fans called shout outs were either unintentional, non-existent, or a result of both parties having drawn from the same, far older, sources. There was one particular instance in Usenet where he went off on a long rant about this after someone asked if he was referencing Return To Zork in an episode.
Draal in "The Long, Twilight Struggle" plays up a very Oz-like attitude, right up to proclaiming "great and terrible".
President Clark's final actions are a mirror of Hitler's final plans right down to the Scorched Earth decree. Of course, Hitler issued his decree to generals and factory managers who immediately ignored it, Clark issued his to automated orbital death rays that had to be taken out by the attack fleet. Then he shoots himself before he can be humiliated by his enemies in public.
In "The Face of the Enemy", when William Edgars tells Garibaldi that by betraying Sheridan he has brought him closer to the truth. Garibaldi responds by saying "The last guy got thirty pieces of silver for the same job."
Vir's conversation with the technomage in "The Geometry of Shadows" includes two: The technomage's name is Elric, and he quotes "an old saying" about not trying the patience of wizards that originates in The Lord of the Rings.
Earthforce Omega-class destroyers, and in particular the rotating section, are similar to the Leonov from Two Thousand Ten The Year We Make Contact. The artist responsible for it intentionally made the rotating section similar, assuming his bosses would catch the joke and have him change it, but nobody noticed and it went into production.
In "Voices of Authority", Ivanova comments to Sheridan about the woman in his quarters trying to seduce him, "Good luck, Captain. I think you're about to go where... everyone has gone before." referencing Star Trek's "To boldly go where no man has gone before."
In another episode, where Babylon 5 has been forced to open a gift shop selling B5-themed merchandise to offset operating costs, Ivanova rants about how Babylon 5's not supposed to be some Deep Space Franchise.