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.
Multiple Shout Outs to George Orwell's 1984: Ministry of Peace, rewriting the dictionaries, etc.
The episode Passing Through Gethsemane has a Biblical shout out in its title, and a plot based on H.P. Lovecraft's The Case of Charles Dexter Ward — right down to naming one of the characters Charlie Dexter.
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.
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."