Darth Vader is perhaps the most important Star Wars character of all time, as well as the most iconic villain in cinematic history. Throughout his time in the Skywalker saga, extended canon, and TV shows, the character has become so layered and incredible for fans to follow. A huge part of this is the various character dynamics he formed ever since he ceased to be Anakin Skywalker.
Vader, of course, does not have what anyone would call friends, but he certainly has allies who, more often than not, fear him. He also has some of the best rivalries in all of Star Wars, even ignoring his internal rivalry with Anakin Skywalker.
Ally - Chelli Lona Aphra
Vader does not have friends, and calling Chelli Lona Aphra, AKA Dr. Aphra, an ally is only loosely true at different points in their relationship.
Nonetheless, it is definitely a fantastic relationship to read in the comics, and through her time with Vader, Aphra became a wildly popular character amongst fans. She has quite the journey with Vader, enlisted by him behind the Emperor's back for secret purposes, literally thrown into space by him, and eventually reunited with him again, with her fantastic story still ongoing.
Rival - Cylo
Sticking with the comics, Cylo was a great rival of Vader's during the 2015 "Darth Vader" comic run from Marvel and was a scientist who believed the future lay in cybernetic enhancements, enhancements he gave himself to become pretty much immortal.
Cylo worked for years on cybernetically-enhanced individuals he believed were capable of dethroning Vader as the Emperor's apprentice. After Vader's failure at the Battle of Yavin, Sidious gave Cylo permission to test his apprentice with Cylo's experiments, resulting in many deaths, including multiple deaths of Cylo over the course of their rivalry.
Ally - Mitth'raw'nuruodo (Thrawn)
Mitth'raw'nuruodo, better known as Grand Admiral Thrawn, worked with both Anakin Skywalker and Darth Vader, as shown in his canon novel series, and it is always great seeing two such incredible characters meet.
In Thrawn: Alliances, the two are put on a mission to Batuu together and end up spending time together above and beyond the said mission. It is by no means the most fleshed-out relationship when looking at just Vader, certainly not like it was in Legends, but throw in Thrawn's time with Anakin and the mutual respect between the two, it is a relationship that is a joy to learn about.
Rival - The Emperor
Darth Vader and the Emperor have such a wonderfully complex relationship through the canon, and while to film viewers it is seen as a pretty strong allyship until Vader realizes how manipulated he has been, it is much more.
The Emperor made sure Vader was always in some form of pain and constantly reminded him of every one of his failures. In return, especially after finding out Luke existed, Vader's faith and devotion to the Emperor came into question. Vader went behind the Emperor's back on numerous occasions for various reasons, as seen in the comics, and on more than one occasion, Vader was tortured by his Master.
Ally - Boba Fett
Another non-friend and mostly business ally of Darth Vader whose help he enlisted for various causes was Boba Fett, an iconic Star Wars character who has become far more fleshed out thanks to the comic and other non-movie content.
Boba Fett is crucial in one of the best Star Wars comic moments ever to date when he delivers the name "Skywalker." to Vader. Then, of course, the two famously collaborated in The Empire Strikes Back, and there is definitely room for more bounties from Vader to Boba in the future.
Rival - Ahsoka Tano
Perhaps the most painful relationship on this list for The Clone Wars fans, the rivalry between Darth Vader and Ahsoka sees the two meet face-to-face only once, but it is still incredibly powerful.
"Twilight of the Apprentice" remains one of the best episodes of Star Wars TV ever, in large part to Vader and Ahsoka. The two finally coming together is packed with tension and heartbreak after it had been teased all season. Their one duel, the unreal dialogue throughout it, and the pain in each moment makes it one of the best rivalries of Vader's and in Star Wars TV thus far.
Ally - Grand Moff Wilhuff Tarkin
Wilhuf Tarkin first met Anakin during the Clone Wars, and he was perhaps the only Jedi he had any shred of liking for, which transferred over to their respective time in the Empire.
Tarkin was one of the few people who knew that Vader was Anakin, which only served to help the mutual respect the two had for one another, with Tarkin being one of the only Imperial Officers Vader did not have much of an issue listening to. The two went on numerous missions together in the early days of the Empire and were two of the Emperor's most trusted underlings.
Rival - Obi-Wan Kenobi
There is something immensely personal about the rivalry between Darth Vader and Obi-Wan Kenobi, with it being obvious that there was a deeper dynamic than just hero vs. villain during their duel in A New Hope.
There is so much history between the two from their time as Master and Apprentice, with Obi-Wan losing Anakin's trust, Obi-Wan being the reason Vader is in the suit, and the two having Vader's first true duel and Obi-Wan's last. There is so much brilliance in their rivalry, brilliance that is likely to be built on in the Obi-Wan series.
Ally - The Emperor
Popping up once again is the Emperor, who is definitely an enemy of Vader, but is also an ally, again playing into the idea that Vader does not have friends; he has people who work with, for, or in Sidious' case, above him.
The two may have been at odds numerous times, and Palpatine may have been severely manipulating Vader and poisoning his mind. But they still ruled the Galaxy side by side, Vader still proved his worth and devotion to the Emperor time and time again, and they were the most successful pair of Sith for years and years.
Rival - Luke Skywalker
The dynamic between Luke and Vader quickly became one of the most complex and brilliant dynamics in Star Wars when Vader revealed the truth about being Luke's father.
It did not immediately change the fact that the two were rivals, though. Luke destroyed the Death Star, and Vader spent a while hunting him down through other means, such as Boba Fett. They had two incredible duels, of course ending in the redemption of Anakin Skywalker, and overall the two are arguably each other's best rivals.