Korra

Korra is the protagonist of The Legend of Korra and is the current Avatar.

Het

 * Amorra - the ship between Korra and Amon
 * Borra - the ship between Korra and Bolin
 * Korroh - the ship between Korra and Iroh
 * Makorra - the ship between Korra and Mako
 * Tahnorra - the ship between Korra and Tahno

Femslash

 * Korpal - the ship between Korra and Opal
 * Korralin - the ship between Korra and Lin Beifong
 * Korrasami - the ship between Korra and Asami Sato
 * Kovira - the ship between Korra and Kuvira

Poly

 * Amorralok - the ship between Korra, Amon, and Tarrlok

Canon
Mako

Korra first had a crush on Mako soon after they met. Mako ended up dating Asami Sato but Korra went after him anyway. Although he initially rejected her, Mako eventually admitted his feelings for Korra and they kissed. Mako's feelings for Korra eventually led to him and Asami breaking up. After Korra lost her bending, Mako confessed his love to Korra and although she initially rejected him, she later kissed him and they started dating.

Korra and Mako dated for over six months. They broke up after getting into a heated argument over their jobs. However, Korra briefly lost her memory of the break-up so Mako played along with her. Korra eventually regained her memory and they decided that it does not work between them. Mako agreed and they broke up for good. They still remained on friendly terms and Korra always sincerely thanked Mako for his help in battle.

Bolin

Bolin first set his eyes on Korra as soon as they met as he could tell that she was special. Korra, however, always had her eyes on Mako instead. Still, Korra was rejected by Mako at first so she went out on a date with Bolin. Korra sincerely enjoyed their date and even told him that he is one of a kind. However, Korra later kissed Mako and Bolin witnessed this which caused him to run off crying. Korra later apologized to Bolin for hurting his feelings and they patched things up. They remained good friends.

Asami Sato

Korra and Asami were first love rivals due to the fact that Asami was dating Mako whom Korra had a crush on. However, Asami took Korra driving and she finally admitted that she misjudged her. Korra later ended up dating Mako but Asami never gave her grief for getting with he ex-boyfriend and being the source of their relationship problems. In fact, Asami sided with Korra against the Equalists which her father was a member of and always aided her in battle.

Korra and Asami were eventually both done with Mako for good and this allowed them to develop their friendship. Even though they were apart for three years at one point, they still remained best friends. Asami allowed Korra to confide her issues in her and although reluctant, Korra eventually did so to Asami and nobody else. After the final battle against Kuvira, Asami admitted that she could not stand to lose Korra and they decided to vacation to the Spirit World together. They held hands and gazed into each other's eyes which marked the beginning of their romantic relationship.

Fanon
As soon as the Legend of Korra was announced, fans began to ship Korra with her airbending master Tenzin despite knowing next to nothing about him. Some fans also shipped her with the moon spirit Yue. Once Mako and Bolin were revealed as characters at the following Comic Con panel, many fans began to ship her with both characters. It turned out that Korra was involved in a love triangle with both characters which fueled shipping wars. Many fans also started to ship Korra with Asami by the end of Book One. Amusingly, they ended up together in the very finale of the series. While it seemed ambiguous at first, many fans could see the romantic context and the creators eventually confirmed this to be the case.

Trivia

 * Nickelodeon initially held reservations for Korra being a female protagonist but eventually changed their minds.
 * Korra is the first known protagonist with a same-sex lover in a western children's show.