Katarina's quote about Cassiopeia is a direct reference to Lady Macbeth's description of how Macbeth should be: "...look like the innocent flower, but be the serpent under't" (I.v.65-66).
Šablóna:W is a constellation in the northern sky, listed by the 2nd century Greek astronomer Šablóna:W.
The symbolic meaning of the constellation Cassiopeia is "Seated Queen", further referenced by her classic skin.
Her ability Šablóna:Ai may refer to Greek mythology, where Šablóna:W is a contagious power that has an independent life of its own. Until purged by the sacrificial death of the wrongdoer, society would be chronically infected by catastrophe.
Cassiopeia is the first champion to currently have a difficulty rating of 100, the second being Šablóna:Ci.
They both were beauties before they got turned into monsters.
They both have relations with snakes. Cassiopeia being half-snake half-human and Medusa having snake hair.
Cassiopeia's ultimate, Šablóna:Ai, turns enemy champions into stone, similar to how Medusa's glance turned her enemies into stone.
Cassiopeia bears resemblance to a combination of a naga, dracaenae, or snake woman, and Medusa.
Cassiopeia may be a reference to Queen Cassiopeia from Greek mythology who boasted of her great beauty. Poseidon punished her by demanding her daughter Andromeda be sacrificed to the Kraken. Perseus, having just slain the Gorgon Medusa, slew the sea monster and saved the princess.
Cassiopeia might also be a reference to Šablóna:W, the last pharaoh of Ancient Egypt. Cleopatra VII was a temptress who seduced various powerful men like Julius Caesar. She killed herself using a bite from an asp.
There's an interesting link between Cassiopeia and summer version of Summoner's Rift - whenever Cassiopeia is present on it, the snakes (normally randomly appearing doodad-creatures in the bushes) don't appear on the map. It also means that Cassiopeia is the first champion to actually affect the appearance of a map during the whole match.
Cassiopeia's dance is the "Weeping Willow" dance, a style of liquid dancing.
Cassiopeia's line, "You found me beautiful, once." may be a reference to the movie Šablóna:W, where the female lead proclaims the same to Ash, the male lead, after she is corrupted by the evil Deadites.
Cassiopeia's picking speech refer to same words of Lady Deathstrike in "X-Men The Animated Series", when Wolverine asks what has she done to herself and she reply same as Cassiopeia.
Cassiopeia's taunt, "Let me help shuffle off your mortal coil." is a reference to Šablóna:W, from the titular character's famous "To be, or not to be" monologue.
Cassiopeia's alternate taunt "You think I'm a freak; let me get on your level" is a tribute to Rioter Phreak's line "Get on my level."
Her Siren skin is a reference to the mythological creatures of Ancient Greece called Šablóna:W, seductresses that enchanted men into the sea to drown.
In Šablóna:Csi skin, Cassiopeia's head is depicted on his shield, most likely referencing their shared Greek relations. From the pose, Pantheon is reflecting Šablóna:Cai, mirroring the Perseus vs Medusa fight of Greek mythology.
Mythic Cassiopeia is a commemorative skin created to celebrate the launch of League of Legend's Greek servers.