Mother and siblings
When Appa was young, he seemed to have a very close bond with his mother and siblings. They would fly in the sky, eat, and play together frequently. However, he never saw his family again after he escaped with his lifelong companion, Aang, and was encased in an iceberg for a century, as they were among the many victims of the Air Nomad Genocide.
Having only known Hawky for a short period of time, Appa was widely unfamiliar with him. When Sokka and Aang left to find Toph and Katara in Fire Fountain City, Sokka ordered Appa to take command of affairs that occurred around camp. Taking this position seriously, Appa settled an argument between Hawky and Momo. The two never formally interacted with each other afterwards following Hawky's leave of absence from the team.
Appa and Momo shared a strong animal bond and companionship with one another. Their close relationship was emphasized when Momo embarked on a journey to search for Appa, who had been captured and separated from the team at that time. Flashbacks depicted the two joyfully flying and eating together. Momo's search came up unsuccessful; he instead resorted to cuddling up with a piece of Appa's fur. Appa and Momo communicated with each other several times, seemingly understanding one another. They occasionally fought over equal portions of food; however, the two maintained a strong bond. Although they had an incredibly quick yet violent battle, complete with samurai swords and armor, this can be disregarded as a factor in their relationship, since Aang saw this while sleep-deprived and hallucinating.
Upon their first encounter, Appa and Nyla were natural enemies, battling each other intensely in the abbey. The shirshu repeatedly lashed out, using the paralyzing neurotoxins within his tongue to immobilize the bison. Appa retaliated by sending powerful gusts of air at his opponent. They eventually became friendlier with each other when they reunited during Zuko's search for Iroh, even nuzzling together and licking each other.
Aang viewed Appa not merely as a pet sky bison and primary means of transportation but as a close friend as well. The two shared a bond that traced back to Appa's years as a calf, where Aang and several other children were told "a sky bison is a companion for life." Appa quickly bonded with Aang, showing his affection by nuzzling and licking him. Aang promised Appa they would always be together. After escaping from the sandbenders, Appa wished immensely to be reunited with Aang. When they were finally reunited after weeks apart, both were overjoyed to see each other.
Appa's loyalty and obedience to Aang was evidenced through his actions; he responded quickly when summoned and never hesitated to battle anyone who attempted to attack Aang.
Appa was the first member of Team Avatar that Hakoda ever laid eyes on, besides his two children. Hakoda sighted Appa when the lone bison was flying in the air in search of Aang. Not knowing the identity of Appa, Hakoda merely gazed in awe at the sight of the giant flying bison.
Hakoda briefly met Appa as a member of Team Avatar when Aang arrived to Chameleon Bay after seeing his vision of Katara in trouble.
From when she first first met him, Katara and Appa shared a strong relationship, with the waterbender expressing little doubt of Appa's flying skills, despite Sokka's claims. When Aang was later captured by Zuko, she trusted in Appa's capabilities to fly and help them rescue Aang. When Aang and Sokka were about to leave with Appa, separating the group, Katara hugged Appa, before being approached by Aang. Their relationship remained firm with Appa deeming Katara a kind caretaker, specifically exemplified when he allowed her and Zuko to ride him even with Aang absent. She showed concern for Appa upon learning of his capture by the sandbenders and joy once reunited with him.
Sokka disliked Appa upon first meeting him, calling him a "fluffy snot monster" after Appa sneezed on him. He was skeptical of Appa's flying abilities until he himself witnessed the bison's abilities. Over time, Appa and Sokka bonded considerably to the extent where Sokka impressed Yue by showing off the bison. Although sometimes critical of Appa's flying skills, the two shared a firm bond. Like the other members of Team Avatar, Sokka was elated when reuniting with the bison outside Lake Laogai. When Aang disappeared under mysterious circumstances, Sokka and Appa searched the skies for Aang.
Appa first met Suki when he, Aang, Sokka, and Katara visited Kyoshi Island. Later, Suki discovered Appa in a shelter after he had run off from the circus. She gently and carefully presented him with berries, and reassured him that she will come right back with help. A few minutes later, she brought along her fellow Kyoshi Warriors to tend to Appa. Gaining his trust, the warriors bathed Appa shortly after approaching him. They washed him and pampered him until he was rid of the needles embedded in his skin and the dirt covering his fur. Minutes later, Azula, Ty Lee, and Mai presented themselves, riding on mongoose dragons. The Fire Nation princess and her team began to battle the warriors attempting to capture them. Appa tried to assist Suki and her warriors, but the fire that Azula produced frightened him. Suki shouted and yelled at Appa to fly away and escape. Clearly torn, the bison flew off into the distance.
Toph and Appa's relationship got off to a rough start after Toph angrily, though correctly, blamed Appa for their situation when they were being tracked: Appa's shed fur was leaving a distinct trail, allowing Azula to track the team's precise location. Being familiar with remaining rooted to the earth, Toph naturally disliked flying. Their relationship improved significantly, however, when they visited Wan Shi Tong's Library, where Toph attempted to engage in conversation with Appa outside the library. She expressed extreme depression after his capture by the sandbenders. Toph and Appa's relationship improved considerably after Appa's return to the group in Lake Laogai.
Unnamed Fire Nation boy
After being captured by sandbenders in the Si Wong Desert, Appa was sold to the Fire Nation circus by beetle-headed merchants. The circus trainer brutalized Appa, refusing to feed him and threatening him using merciless displays of firebending. On one occasion, when the circus trainer left briefly, a young boy secretly entered the circus tent and fed Appa a bale of hay. Appa licked him to show his appreciation. The boy fled the circus tent upon the return of the circus trainer. During a circus performance that evening, Appa was dressed in a ridiculous costume and cruelly forced to obey the trainer's commands. Seeing the torture the bison was forced to endure, the young boy encouraged Appa to escape. The boy reminded Appa of Aang, and the sky bison followed his advice, flying away from the circus.
Having previously been an enemy of Team Avatar, Zuko was originally a natural enemy of Appa. In Ba Sing Se, Zuko freed Appa from the Dai Li headquarters, gaining the bison's trust. Appa was the first to approve of Zuko's acceptance into Team Avatar, expressing this approval through licking him. Appa's approval of Zuko was one reason why Aang and the others accepted him into the group. Prior to the arrival of Sozin's Comet, Appa grew comfortable with Zuko's presence to the extent where he permitted Zuko to steer him along their travels.
After determining that Appa's perceived ferocious nature would prove to be too much of a burden to handle, the beetle-headed merchants sold him to a traveling circus. There, Appa was placed under the care of a cruel and merciless circus trainer who promised to break the bison to his will. The trainer was abusive toward Appa, keeping him locked in a tight cage with his legs chained together, refusing to feed him and threatening him with firebending. On the night of a circus performance, the trainer dressed him in a ridiculous outfit and once again displayed his abusive nature, frequently striking the bison with a fire whip. Appa was able to escape the circus that evening. His treatment at the circus caused him to become pyrophobic.
The Sandbender Tribes of the Si Wong Desert seemingly viewed Appa as valuable from early on, surrounding him outside the Misty Palms Oasis before being chased off by Professor Zei. Later on, while all of Team Avatar, except for Toph, and the professor were in an underground library, the sandbenders arrived at the scene, riding in on sand-sailers. There, they proceeded to use ropes to try and subdue the bison in a clear attempt to capture him. Toph tried to hinder their progress, but was unable to launch effective attacks due to her vision being impaired by the shifty sand. After a long struggle with Appa putting up a good fight against the sandbenders, who were led by a young man called Ghashiun, the tribe members were finally able to pin him down and capture him.
Appa was driven away deep into the desert where his saddle was then ransacked for any valuable possessions. He displayed a fierce attitude toward the sandbenders both during and after the fight, continually growling at them in anger. He was eventually sold to the beetle-headed merchants.
Long Feng was a fierce enemy of Appa, having been directly responsible for his capture in Ba Sing Se. When Long Feng and the Dai Li discovered Appa searching for Aang, they imprisoned the bison and harbored him in their secret underground base beneath Lake Laogai until Zuko liberated him. When a battle ensued between Team Avatar and the Dai Li, Appa bit Long Feng on the leg and tossed him into the lake. Appa and Long Feng encountered each other later in Earth King Kuei's throne room when the team was trying to alert the king of the secret conspiracy; the bite marks on Long Feng's leg were used as evidence and convinced the Earth King to investigate further.