Star Wars continues to grow, especially not with its various Disney+ shows, Andor being the newest of these. With all the new content coming out, it's easy to forget where it all began in the original trilogy.
There were many characters in the original three movies, all of whom needed to work together in order achieve their various objectives.
Many of these characters as well had to have a certain degree of loyalty to both their colleagues and their respective factions. Without that loyalty, things wouldn't have gone as well.
Lando Calrissian
The sharply dressed Baron Administrator of Cloud City became a loyal general in the Rebel Alliance, but his previous actions bring his loyalty ranking down quite a bit.
Lando is forced to help the Empire set a trap for Han Solo on Cloud City in The Empire Strikes Back, which leads to Han's capture and imprisonment. After it was clear that the Empire was not going to leave Cloud City in his control, Lando turned on them and later helped Luke free Han from Jabba the Hutt. While these earlier actions left his loyalty in question, his smooth talking and daring wit made him an invaluable ally in the battle against the Empire.
Darth Vader
Darth Vader would easily be one of the Emperor's most loyal henchmen - if not for his steps towards his redemption.
Prior to Return of the Jedi, Vader was bent on turning Luke, his son, to the Dark Side. But after seeing him getting tortured by the Emperor, he switched sides, turning on the Emperor and easily defeating him. This quick change in loyalties would be Vader's end, but also showed that his loyalties could change. All he had to do was break free from the Emperor's influence and return to the Light Side of the Force.
Han Solo
Han is certainly a loyal friend, that much is obvious. But his main loyalty, at least when audiences are first introduced to him, is to himself.
As a smuggler with a long list of crimes that he'd be arrested for on Earth, Han cares much more about getting the money he owes out and back to Tatooine. But when push comes to shove, he is shown to be give up his own self-interest in order to save his friends. That being said, he's certainly still a self-serving man that does still care more to some degree about what will benefit him the most, something that he gradually loses over time.
C-3PO
A standout character with appearances in nearly every film in the franchise, C-3PO may be a nervous wreck most of the time, but this does not affect his loyalty in any way.
He is, at heart, a protocol droid, and as such, has some degree of programmed loyalty to his master and the Rebel Alliance. While he is certainly a blabbermouth and may accidentally reveal top secret information to the wrong people, he is at heart a loyal droid that also understands the danger that the Empire holds and why they have to go down.
Obi-Wan Kenobi
Obi-Wan "Ben" Kenobi was once a Jedi Master, but soon became one of its last survivors. Following this, his new mission became to protect Luke at all costs.
Obi-Wan would sacrifice his very life in order to protect Luke from the evils of Darth Vader. As a Jedi, his loyalty has no bounds. He is willing to do whatever it takes to ensure that his mission is complete and Luke is safe. When he dies, he continues to guide Luke as a spirit, showing that his loyalty remains true even years after his death.
Luke Skywalker
Luke started out as a farm boy from Tatooine, but soon grows into a powerful Jedi and member of the Rebel Alliance.
Right from A New Hope, it's clear that Luke hates the Empire and wants them to go down. And this is just the first step in his hero's journey. As he joins the Rebellion, he becomes a loyal rebel warrior and their best pilot. There isn't even a hint of any sign of wavering loyalty. He even turns himself in to Darth Vader in an attempt to save Leia from the Dark Side.
Princess Leia
Leia has suffered many awful things during the course of the franchise. But nothing could ever break her loyalty to the Rebellion.
Not even torture at the hands of Darth Vader and Grand Moff Tarkin is enough to make her break. She's incredibly strong, unwilling to give up the location of the Rebel base on Yavin IV. Seeing her home planet getting blown to pieces by the Death Star just makes her even more determined to bring the Empire down and furthers her loyalty to the Rebellion.
R2-D2
This little blue droid has seen it all - and his no doubt one of the most loyal characters in the entire franchise.
R2 has often saved Luke and the others multiple times, usually in simple, easy ways. Though, like with C-3PO, much of R2's loyalty is pre-programmed. But unlike C-3PO, R2 is more daring and helpful, always offering up solutions to get through locked doors or shut down important equipment. There are very few friends in the Star Wars Universe more loyal than R2.
Grand Moff Tarkin
Tarkin is one of the most evil villains in the Star Wars Universe, as well as one of the Emperor's most loyal and trusted henchmen.
Tarkin takes command of the Death Star project and is in such a high state of authority that even Darth Vader most follow his orders. He is completely dedicated to the Empire and its rule over the galaxy, willing to blow up entire planets in order to keep order in the galaxy. He served the Emperor loyally and faithfully until his death on the Death Star after its destruction.
Chewbacca 
When it comes to loyalty in the galaxy, there is no species that make more loyal friends than Wookiees. And the most famous Wookiee of them all is, of course, Chewbacca.
After Han Solo saved his life and helped to free him from the Empire, Chewbacca proclaimed a life debt to him, sealing his loyalty forever to Han. The two went on to become lifelong friends and helped participate in the downfall of the Empire. Chewbacca's loyalty is never in question, and he stays true to himself and his friends no matter what happened. There is no single warrior as loyal as him.