The method of constructing Hosts, as shown in the opening titles, resembles the description of how robots were constructed in R.U.R.
The Host construction is also very similar to the creation of Synths in Fallout 4. Additionally, the robotic technician uniforms are strongly reminiscent of those worn by the Institute.
Ford is shown to keep various host faces displayed in his office; one set aside on its own table bears a striking resemblance to Sander Cohen, an infamous antagonist in Bioshock (which also happens to be about an isolated technological kingdom ruled by an industrialist genius with a God complex).
The arc words, "These violent delights have violent ends" come from Shakespeare's Romeo and Juliet. And as noted within the show, Ford programmed some of the Hosts to make plenty of references to Shakespeare.
One of the first lines of the pilot, is 'Can You Hear Me?', said by a human to a Host. It often happens to be the opening words of another AI when starting conversations with humans on Person of Interest, also created by Jonathan Nolan. Also, the bird that Felix is working on "Contrapasso", is a finch. And as the first season ends with the Hosts awakening and starting their rebellion, the music is a cover version of Radiohead's Exit Music (for a Film), which Person of Interest used at the end of season 3 when Samaritan awakened. At several points, hosts also ask 'is this now? Or one of my memories?', which is said by the Machine in the series finale.
In "The Stray", the woodcutter is shown to have a programmed hobby of woodcarving. Two of the carvings, one of a bear and another of a turtle, have etching of the constellation Orion on them. The bear and the turtle are major symbols in The Dark Tower by Stephen King, where they serve as metaphorical and literal guardians of one of the eponymous Tower's six beams. Considering that one of the show's creators previously worked on trying to get the film adaptation of the series out of Development Hell, it's not a stretch to say the symbolism was deliberate, especially considering how similar Westworld is to The Dark Tower in setting and themes.
Logan is made a major ("or a general, or whatever") with a pin that looks remarkably like the one for the Hand of the King on Game of Thrones, another HBO show.
In the first season finale, Dolores describes to the Man in Black (who is revealed to be William) creatures that once roamed the earth the "size of mountains" who later became "bones and amber", an obvious reference (and threat) about humanity going the way of the dinosaur. The reference to "bones and amber" quite specifically brings to mind another Michael Crichton story about a theme park's attractions going haywire.
In the same episode, the tactical response team makes a sweep through the floors. Hector hides among inactive Hosts, but slowly moves his eyes as they go by, reminiscent of the famous scene with Del Spooner and Sonny in I, Robot.
Dr. Ford at one point quotes his distant colleague Frankenstein: "One man's life or death were but a small price to pay for the acquirement of the knowledge which I sought; for the dominion I should acquire."
In Season 2, GiancarloEsposito once more plays the head of a huge criminal empire in a semi-rural desert environment, and is even doing Gus Fring's accent during his scenes as the new El Lazo.
Emily in Season 2 is revealed to have gone under the alias "Grace" during her time in the park.
James Delos' descent into madness as a malfunctioning Host copy is more than a little similar to that of Pinbacker's own insanity in Sunshine. The actual scene with him and William is shot in a manner reminiscent of the climatic conversation in Event Horizon between Miller & Weir.
In the first episode of Season 3, Caleb's first scene of waking up is a homage to the Major's scene of waking up in Ghost in the Shell.
The host sinking down the water, revealing its metallic face in Season 3's opening is also a homage to Ghost in the Shell.
In season 3, episode 2 when Bernard and Stubbs are walking through the Westworld offices, they come across two techs discussing how to sneak a host out of the park to a buyer- the camera swings around to show Drogon, from Game of Thrones with the techs. The techs are also played by the Game of Thrones showrunners David Benioff and DB Weiss
"Ride of the Valkyries" plays when Caleb gets into a shootout during a drug trip. Apocalypse Now, anyone?
It's eventually revealed in the season three finale that the rich genius and supposed Big Bad who created a revolutionary new artificial intelligence has in fact relinquished his free will and begun to obey the commands of his superior creation. Almost the exact same thing happens in the ending of Upgrade.
In the third season finale, Bernard and Stubbs take shelter in a roadside motel that bears a striking resemblance to the Bates Motel from Psycho. The fact that Bernard is both fixated on a homicidal woman — who might as well be his mother — and dealing with Split Personality issues just makes this even more appropriate.
The last scene of the Season 3 finale shows Caleb and Maeve watching the buildings explode is similar to the ending in Fight Club.
This show decides to show what happens when all of humanity's fate is left to a machine, predicting paths from correlated past information. Seems like Jonathan Nolan decided to show a darker version a previous show he created in this latest series.
There are parallels between the Man in Black, played by Ed Harris, and Christof from The Truman Show, also played by Harris. Both stories revolve around individuals discovering they live in an artificial world created for the entertainment of others, and the Harris character in both makes the cynical observation that the outside world is no more a place of truth than the artificially created one:
Christof: "There's no more truth out there than there is in the world I created for you: same lies, the same deceit."
Man in Black: "You helped me understand this world is just like the one outside: a game, one to be fought, taken, won."
are similar to the Christ Cunningham-directed music video for Björk's "All Is Full Of Love."