Since the two were young, Elsa and Anna have always been the best of friends and loved each other dearly. The two enjoyed playing together, and Anna loved it when Elsa used her snowy/frosty magic to create a winter wonderland. However, after Elsa accidentally hit Anna with her cryokinesis and almost killed her, Elsa has been too scared to go near Anna, out of fear her increasingly strong abilities could harm her again. While Elsa's desire to stay away from Anna was out of her love for her, Anna felt distanced from her and constantly tried to reconnect with Elsa without understanding or knowing about Elsa's ice and snow magic, as her memories of Elsa's frosty magic were erased after the troll king revived her.
During the coronation party, the two seemed to temporarily reconnect as they enjoyed themselves, and Anna suggested things could go back to how things used to be. Unfortunately, Elsa remembered how she hurt Anna, and decided things could never be the same. When Elsa's powers were revealed to the kingdom after the two got into an argument about Anna's engagement to Hans (despite having only known him for the day) and she ran away, feeling responsible for what had just transpired, Anna was the one to volunteer to get her back and defended her by saying "She's my sister. She would never hurt me." When she got to Elsa's palace, she tried to have Elsa come back home to fix the eternal winter she cast on the kingdom, but couldn't persuade her, as Elsa felt the kingdom would be safe away from her, and because she felt she couldn't fix what she had done.
Nonetheless, her intense and genuine sisterly love for her older sister prevailed and proved to be the thing Anna held most dear to her, shown best when she stepped in front of Elsa to protect her from Hans' killing strike, sacrificing her own life in the process. This demonstrates just how deep Anna's love for Elsa is and that no matter what happens, their sisterly bond is the most important thing to her. This act of true love is also ultimately what saves Anna from Elsa's curse, as Olaf informs that Anna's actions were an act of true love, and this allows Elsa to finally get rid of the storm, returning to her rightful place as queen and restoring her bond with Anna.
Elsa and Anna truly care and love each other, and while Elsa was too scared of hurting Anna to get close to her, and Anna was at times somewhat pushy and insistent on helping Elsa (which could at times make things worse), and both are complete opposites, the two will always love each other and do anything for the sake of the other's happiness.
In the shorts Frozen Fever and Olaf's Frozen Adventure, Anna's restored bond with Elsa grows stronger as the two catch up on the yearly celebrations they missed in the past, such as birthdays and the holidays. The former shows Anna's growing concern for Elsa's health while celebrating her birthday and ends with Anna remarking that taking care of her sister is the best birthday present ever. The latter reveals that Anna had made gifts based on Olaf and presented them to Elsa every Christmas as a reminder of their childhood and the love they have for each other, leading the sisters to realize that Olaf is their tradition.
The storybook A Sister More Like Me showed a side of Anna and Elsa's sisterly relationship. Both sisters once longed to have siblings that shared more common interests with one another. As Elsa was regal, elegant and poised, Anna was spontaneous, rambunctious, and full of life. Because of the isolation, however, they didn't realize their desires to have siblings just like them weren't what they truly desired. Once things were patched up and Arendelle's peace was restored, the book shows that Anna and Elsa were more than happy loving one another for who they are, Anna admiring Elsa's power and intelligence, and Elsa admiring Anna's tendency to always listen to her heart and ways of showing her strong and close love for those close to her.
On the night Anna was injured by her sister's magic, her parents, King Agnarr and Queen Iduna brought Anna to see Grand Pabbie, who healed Anna by removing her memories of Elsa's magic. Despite her recovery, Agnarr and Iduna were concerned for Anna's safety, and so they separated her from Elsa until the latter garnered complete control over her powers. Due to having limited contact with Elsa over the years, Anna became quite close to her parents, and was devastated when they died at sea, and Anna now was truly alone.
Initially, Kristoff only accompanied Anna on her trip to retrieve her older sister because Anna paid him with the pickaxe, rope and bag of carrots he wanted but couldn't himself afford, as Trader Oaken increased their price. He found Anna's quick engagement to Hans ludicrous, and questioned her judgment. He was also annoyed when he lost his sled due to having to accompany Anna on her journey to find Elsa, and only continued to accompany her after Sven convinced him. However, as the two spent time together and he began to see more of her fiery and sweet character, he became smitten with her, and it seemed reciprocated, but both continued to deny and ignore this because of Anna's previous engagement to Hans.
This became apparent throughout their journey, and more apparent as Kristoff was tending to her while her health was deteriorating due to Elsa's curse, and they reached the troll cave, where the trolls teased the two about their relationship. When Kristoff managed to return Anna to the castle, he was clearly still worried about her health and heartbroken over having lost Anna to Hans. Unfortunately, he was too dense to realize his feelings until Sven helps him. Suddenly, as the storm worsens around the castle, Kristoff realizes Anna is in trouble, and tries to help, but Anna instead goes to save Elsa, her spells petrifying her into solid ice. He mourns losing Anna, and is overjoyed when he saw that she was revived due to her act of true sisterly love for Elsa.
When Hans was waking up after being knocked unconscious by his killing blow being reflected by Anna's frozen body, Kristoff was angry enough over Hans' treachery to attempt to clobber him. However, Anna stopped him so she could confront and punch Hans instead. After Elsa stopped the storm, Anna gave Kristoff a new sled to replace the old one, and he was so happy, he said he could kiss her. It is then shown that Kristoff is the shy one in their relationship, as he becomes awkward about what he says, and it is Anna who instigates the kiss. After Hans and the Duke of Weselton are deported, Olaf and Sven enjoy summer together, and Anna buys Kristoff his promised new sled. Upon informing him that Elsa had named him "Official Arendelle Ice Master and Deliverer", he attempts to decline both the sled and the title, too modest to accept, but Anna points out that this is a direct order from the queen. When she asks what his thoughts on the sled are, Kristoff picks up Anna and twirls her around in his arms, exclaiming he loves it, and that he could kiss her. He immediately puts her down, and stammers awkwardly that he'd like to, among several sentences of nonsense, leaving him embarrassingly flustered before Anna kisses his cheek, saying to Kristoff "We may." Kristoff smiles and kisses her, initiating their relationship.
In Frozen Fever, Kristoff presents Anna her birthday cake as he proclaims his love for her, and Anna returns those sentiments with an elated, heartfelt grin.
Alies & Friends
Olaf was based on a snowman Anna and Elsa created when they were young and Elsa appears to have created him as a reminder of her happy childhood memories. When Anna first meets Olaf, she is initially creeped out by the talking snowman, but then quickly realizes he is the same Olaf from her childhood, and becomes good friends with him. This is shown, as she supports Olaf's dreams of summer and insists Kristoff to not ruin it for him, and when she was angered with Marshmallow throwing him and was willing to confront Marshmallow over the matter.
Olaf returned her friendship as he tried to stall Marshmallow, so Anna and Kristoff could escape, and again demonstrated when he told Anna to run from Kristoff when he brought them to his family of "rocks" (who were actually the trolls disguised as rocks), and Olaf thought Kristoff was crazy, telling Anna "Because I love you, Anna, I insist you run." He was even willing to melt to death in order to create a fire to warm up Anna to slow the freezing curse placed on her by Elsa, while comforting her over Hans' betrayal. He was also the one to teach Anna what love was after she felt disillusioned due to Hans' treachery, and was the one to inform everyone how it was Anna's act of true love that saved her from dying.
Overall, Anna and Olaf share a very strong friendship which is made stronger by the fact that they both care for Elsa, and Olaf is a symbol of Anna and Elsa's strong sisterly bond.
Sven is Kristoff's best friend/pet reindeer, and he seems just as loyal and friendly to Anna as he is to Kristoff. Sven helped Anna to rescue Kristoff when he was about to fall off the cliff when they escaped the wolves, and she had also bought the carrots that Kristoff had intended to buy for him when at Oaken's store. When Kristoff dropped Anna off at the castle to be saved by her "true love" Hans, Sven appeared torn between with Anna and leaving with Kristoff, and even attempted to force him to go back to her.
Though Pabbie is far from the most recurring figure in Anna's life, he's been extremely prominent for many years, going all the way back to her childhood. Pabbie's responsible for saving the princess' life not once, but twice. Those instances were the night he healed the princess' injury due to Elsa's powers, and again during Anna's adulthood, where he revealed the remedy that would thaw her infamous frozen heart. Though their interactions were brief, Pabbie seems to pose as a grandfatherly figure to Anna, with both moments he's on-screen showing a sense of pure care and love, as if she was his own family. This could also tie-in to the fact that the wise, old troll is the adoptive grandfather of Kristoff.
Initially, when Anna first met Hans, she became instantly strongly romantically attracted with his good looks and charm. As the two became more acquainted with each other and their lonely pasts, the two soon shared a romantic duet which ended with Hans proposing to Anna, which she gladly accepted in a heartbeat despite having known him for a day. While Anna was away, she proclaimed that Hans would be in charge during her and Elsa's absence. While it seemed during Anna's absence that he truly cared for and loved her, when Anna returned to Arendelle to receive a true love's kiss from him in the hopes of healing Elsa's frosty curse inflicted on her, Hans revealed he had never loved her in the first place and how he only planned to marry her to become King of Arendelle and kill Elsa to ensure this.
He left Anna to literally freeze to death as he went to kill Elsa, and any feelings Anna had for him disappeared. She managed to interfere with his plans and save Elsa by using her frozen body as a shield to block his killing blow, and got her revenge on Hans by punching him off the ship they were on. It should be noted that due to her years of loneliness and desperation for love, Anna's "love" for Hans was nothing more than a small crush based on his outward appearance and her belief that she would not have another chance to find someone else, while her feelings for Kristoff were genuine and based on real love. Even Hans has stated how she was so desperate for love that she was willing to marry him just like that. It is also apparent that there is no (longer any) affection between the two sides, as Anna hates Hans for the monster he truly is, and Hans never truly cared for Anna at all, but was instead using her infatuation for him to get Arendelle's throne and was willing to let her die to further his own fiendish schemes.
The novel A Frozen Heart further explores the relationship between Anna and Hans.
When Anna refused to leave without her, Elsa created the giant snow monster Marshmallow, and he threw Anna, Kristoff and Olaf out of her palace, telling them to go away. He threw Olaf, which angered Anna into Telling him that it's not nice to throw people. While getting ready to throw the snowball at Marshmallow, Kristoff stopped her, telling her to leave the snowman alone, but gave Kristoff the impression that she was calm. Anna then threw the snowball at the giant snow monster anyway. Angered by this, Marshmallow chased after them, though Anna was able to launch a pine tree into Marshmallow's face. While Anna and Kristoff were descending down the cliff, Marshmallow started to pull them back up, and shouted at them to not come back. Anna, out of fear, replied that they wouldn't, and then cuts the rope so that she and Kristoff could get away from the snow monster.
Marshmallow was important for being another one of Elsa's snow creations that represented an aspect of her relationship with Anna. While Olaf represented their need to be together, Marshmallow represented Elsa's desire for separation to ensure Anna's safety. However, Marshmallow also represented the fact that regardless of Elsa's intent, she ultimately ended up hurting Anna anyway, both physically and emotionally.
The Duke of Weselton was polite to Anna as with her sister, and even danced with her (after Elsa told him her sister dances) and asked her if she know why the castle gates were shut, but she said she did not know. When Elsa's powers were revealed, he was briefly hostile towards her, asking if she has magic like her sister, but Anna and Hans reassure him that she is ordinary. Anna and Hans argue with the Duke that Elsa was not a monster, but the Duke refuses to believe them. When Anna says she will go to get Elsa, the Duke quickly agrees, showing that by this point, he was not too concerned with Anna's safety. When Hans was giving out necessities to Arendelle's citizens, the Duke showed that he did not trust Anna, believing that she and Elsa were conspiring to doom them all. But in the end, the Duke showed that he had began to care for Anna a little, as he showed grief when Hans lied to him and the other dignitaries that Anna had been "killed" by Elsa, where the Duke was the first to say that there was no doubt that Elsa was a monster.