There are almost too many allusions in this novel to list. I'll give you a few to help you get started.
"It is computed that eleven thousand persons have at several times suffered death, rather than submit to break their eggs at the smaller end." (Very end of The Hearth and the Salamander.)
This quote is from Jonathan Swift's Gulliver's Travels. It refers to a land where Gulliver travels and the emperor has decreed that everyone break their boiled eggs at the small end. This decree leads to a war. Swift himself was being satirical and Bradbury likely uses this reference to emphasize how far humans will go to avoid conformity.
We cannot tell the precise moment when friendship is formed...so in a series of kindnesses there is at last one which makes the heart run over." (Beginning of The Sieve and the Sand)
This quote is from James Boswell's Life of Dr. Johnson and it parallels Montag's relationship with Clarisse. He cannot understand why/how such a strange girl is bringing so much joy into his life.
Consider the lilies of the field... (The Sieve and the Sand, while Montag is on the subway.)
This is an allusion to Jesus' Sermon on the Mount, found in Matthew 6. In context it is a reminder not to worry about material things, and in the context of the novel, it likely refers to Montag's realization that his spiritual hunger is greater than his material need.
Burning Bright (title of Part Three)
Reference to William Blake's "The Tyger." In the poem, the tiger is a symbol for a world where evil reigns, but it goes on to discuss that everything in existence has a dual nature. This title for Part 3 is appropriate therefore, because as the world burns from the war at the end of the book, there is a sense of hope for the future.
There is no terror, Cassius, in your idle threats, for I'm armed so strong in honesty... (middle of Burning Bright, Beatty vs. Montag)
Beatty's reference to Shakespeare's Julius Ceasar here is a bit ironic as he is taunting Montag (who here would assumedly be Ceasar) and making fun of his new found sense of right versus wrong and "honesty."