Kara Zor-El

Kara Zor-El (or Supergirl) is the main character on CW series Supergirl and the Arrowverse fandom.

Character
At 11 years old, Kara was sent to Earth in a pod by her parents, to avoid dying in the destruction of Krypton and watch over her infant cousin, Superman. A meteor hit her pod and she was stranded in the Phantom Zone for many years, only to be released eventually by the activities of Indigo, an evil synthetic life-form.

Kara was met with a grown Superman upon her crash on earth and he found a family to adopt her, leaving Kara without a mission to mourn her parents and the destruction of Krypton, and figure out how to live a new life on Earth.

As an adult, Kara takes a job as an assistant to a media mogul in National City and eventually develops a taste for journalism herself. At work she also meets and grows close friendships with James Olsen and Winn Schott. Her sister Alex facing imminent death in a plane crash causes Kara to reveal her powers and take up the mantle of Supergirl.

Canon
James Olsen

Kara and James meet when he is offered a job as head of the Art Department at Cat Co. and Kara is instantly taking by his kind nature and warmth. She immediately gets a crush on him, but doesn't reveal herself when James' ex Lucy Lane comes to town and the two reconcile.

Mon-El

Het

 * Karadam – the ship between Kara and Adam Foster
 * KaraMel – the ship between Kara and Mon-El
 * Karolsen – the ship between James Olsen and Kara
 * Karay – the ship between Kara and Ray Palmer
 * Superarrow – the ship between Kara and Oliver Queen
 * SuperFlash — the ship between Kara and Barry Allen
 * Superlord - the ship between Kara and Maxwell Lord
 * Supersteel — the ship between Kara and Nate Heywood
 * Supervibe - the ship between Kara and Cisco Ramon
 * SuperWave - the ship between Kara and Mick Rory
 * Winnara – the ship between Kara and Winn Schott

Femslash

 * Snowgirl — the ship between Caitlin Snow and Kara
 * Supercanary — the ship between Kara and Sara Lance
 * SuperCat – the ship between Kara and Cat Grant
 * SuperCorp – the ship between Lena Luthor and Kara
 * SuperLane – the ship between Kara and Lucy Lane
 * Superreign – the ship between Kara and Sam Arias
 * Superwatch — the ship between Kara and Felicity Smoak

Poly

 * Karolswinn - the ship between Kara, James Olsen and Winn Schott
 * Superreigncorp – the ship between Kara, Lena Luthor and Sam Arias

Family

 * Kalex – the ship between Kara and Alex Danvers