Pre-Crisis on Infinite Earths:
* The original Supergirl (Kara Zor-El) was killed in the first "Crisis on Infinite Earths"** event (1985-1986). She died saving the multiverse from the Anti-Monitor, sacrificing herself to save her cousin, Superman.
Post-Crisis on Infinite Earths:
* A new Supergirl (Linda Danvers) was introduced. She didn't die, but she was killed by the villain Darkseid in "Final Night" (1996) during a battle for the universe.
* However, she was later resurrected and continued her heroic career.
New 52 & Rebirth:
* The New 52 introduced a new version of Supergirl (Kara Zor-El) who has remained alive throughout her various stories, and she survived the "Death of Superman"** event where her cousin was killed.
* In the Rebirth era, she has remained alive, despite facing various challenges and hardships. She even got married to a member of the Legion of Super-Heroes, Mon-El.
Other notable "deaths":
* Supergirl has been seemingly killed on multiple occasions, but these were typically temporary. Some notable examples include:
* The "Reign of the Supermen" storyline where she was seemingly killed by Doomsday.
* She was also "killed" by Cyborg Superman in "The Adventures of Superman".
Overall:
Supergirl has had a long and complicated history with death in the comics. While she has faced many threats, and even been seemingly killed a few times, she has always come back stronger. Her current iteration is alive and well, and she continues to fight for justice alongside her cousin, Superman.