To be fair, his dead dad asked him to...

His father's murder, at the hands of his uncle and mom.

He killed his uncle and mom, and his sister committed suicide. You can argue that Ophelia was driven to suicide, but that's not entirely on Hamlet. He might have saved her if he wasn't so consumed with vengeance, but that's not how the story goes.

Poor Yorick. Where be his jibes now?

It was the vampires. They should have stayed at their home base.