Body Repair Shop
In both the 1973 film and the TV show, Hosts are repaired in hospital-like settings. Employees are dressed in scrubs and perform surgery on the hosts.
Westworld in the TV series operates similarly as Delos in the film. Guests are able to do anything they want with the hosts, guns are unable to harm guests and hosts are forbidden from killing guests.
In addition, like Delos in the Westworld Film, Delos Destinations, Inc. runs different themed parks near Westworld.
The Gunslinger on Sub-Level B82
While looking through Sub-Level B82, Bernard's flashlight briefly illuminates The Gunslinger, from the 1973 film Westworld. The figure seen in the episode is a statue, made by Nick Marra. There's a link to his (delighted) instagram post on the subject here.
William and Logan
William and Logan have some similarities to Peter Martin and John Blane respectively. (Young) William, like Peter, is a first time visitor to the park, while Logan, like John, serves as a guide to William. Peter was also recently married to a woman named Julie, whereas William is engaged to be married, to a woman named Juliet.
In addition to anachronistic covers of popular music and references to the music of Western films, Ramin Djawadi's soundtrack for the HBO TV series also includes some references to Fred Karlin's soundtrack for the original film from 1973.
The most obvious examples of this are the tracks Nitro Heist and Sweetwater, two related leitmotifs with a very similar underlying melody. Both seem to be based on two equally related tracks from the 1973 soundtrack, Chase from Westworld and Chase from Westworld - Part 2. These are heard during the famous chase sequence of the film, when The Gunslinger pursues the shocked Peter Martin on horseback and on foot through much of Westworld and the whole Delos resort. The melodies of the two TV series' tracks have a slower tempo than the tracks from the original film.
Another theme from the original film reinterpreted and adapted for the TV series is The Gunslinger. This is a sinister-sounding leitmotif for the titular character, the film's main robot antagonist. It features the use of odd sound effects and ambient elements, including artificially sounding reverbations, ripples and thuds that also make an appearance in the two Chase themes. These thudding sounds make an appearance in the series' major host theme, Freeze All Motor Functions.
Though the electronic ambient tracks Robot Repair from the film and Freeze All Motor Functions from the series do not seem to share a melody, they are otherwise similar compositions, and commonly used as the leitmotif of the robots or hosts. In a reversal to the other music reworked for the series (which is usually slower than the originals), the film's robot leitmotif is slow, mysterious and contemplative, while the series' host leitmotif has a faster tempo and a darker, more brooding quality.
Fleeing from deadly robots, from one park to the next
The final third of the original film focuses on Peter's frantic escape from Westworld, with the merciless and deadly Gunslinger hot on his heels. John is shot dead by The Gunslinger, prompting Peter to fully realise something has gone wrong with the robots' programming, and attempt to flee. Resting briefly, he stumbles upon a stranded technician who offers him some vague advice for dealing with the Gunslinger. As the pursuit continues, Peter eventually crosses the official boundaries of Westworld and enters the territory of Roman World. The Gunslinger continues to track him through Roman World, follows him through the Delos staff areas and catches up with him in Medieval World. Peter manages to narrowly defeat him and survive.
In the second season episode Virtù e Fortuna, the opening, pre-credits plot focuses on Emily during her visit to The Raj. Once the host uprising begins, Emily and Nicholas discover dead guests, prompting Emily to insist something has gone wrong. They are attacked by their host guide Ganju, who kills Nicholas. Emily shoots Ganju in self-defence and decides to run until she reaches the boundaries of Westworld. Nearing them, she briefly rests, but comes under a surprise attack by a Bengal tiger host, and resumes her escape. The tiger crosses the official border of The Raj and follows her into Westworld. Emily manages to narrowly defeat the tiger by shooting it before they fall into the water reservoir on the borders of Westworld.
Fittingly, Emily is the daughter of William, the series' counterpart to the film's Peter (who is a similar inexperienced newcomer during the first third of the film).