General definition of the discriminant

Question

There is a notion of the discriminant of

1. polynomials
2. quadratic forms
3. finite separable extensions of Dedekind domains (e.g., algebraic number fields)

I don't know much about 2, but I think that 1 and 3 measure ramification.

Do these three types of discriminants have a common generalization? Is there some general notion of what a discriminant is?