How Did Dobby Die?

Death eater Bellatrix Lestrange hurled her knife at Dobby and Harry as they "apparated", hitting him and fatally wounding the elf. He was buried without magic, in a grave marked "Here Lies Dobby, A Free Elf".

Why did Dobby kill himself?

After Harry helps him win his freedom from the sinister Malfoy family, Dobby pledges his loyalty to the Hogwarts student. Eventually, he sacrifices himself so that Harry and his friends could go on to save the world from Lord Voldemort.

What killed Dobby?

Dobby was murdered by Death Eater Bellatrix Lestrange in the course of rescuing several prisoners from Malfoy Manor. His burial was conducted by Harry Potter, and his eulogy was given by Luna Lovegood, though the others he rescued also gave a few words of gratitude and respect.