3denali:

Carlisle: I was attacked and turned during a raid on a vampire coven

Esme: Carlisle turned me after a suicide attempt spurred by the loss of my child

Edward: I nearly died from the Spanish influenza after watching my parents die from the same pandemic.

Rosalie: I was raped and beaten by my drunken fiancé and his friends and left to die

Alice: I was hunted by a tracker after being institutionalized by my own family and turned for my own safety

Jasper: I was turned to be used to create an army and was forced to slaughter newborns

Emmett: bear.