In Much Ado About Nothing, Don John is a stock, flat, static character.  He is a villain because he admits it to Conrad, another villain:

I had rather be a canker in a hedge than a rose in
his grace, and it better fits my blood to be
disdained of all than to fashion a carriage to rob
love from any: in this, though I cannot be said to
be a flattering honest man, it must not be denied
but I am a plain-dealing villain. I am trusted with
a muzzle and enfranchised with a clog; therefore I
have decreed not to sing in my cage. If I had my
mouth, I would bite; if I had my liberty, I would do
my liking: in the meantime let me be that I am and
seek not to alter me.

Why is Don John so villainous?  He's a bastard.  Really, he is:

Benedick says, "I must discontinue your company: your brother the bastard is fled from Messina:"

Bastards are sons without legitimate fathers.  They were the lowest status of males in Shakespeare's day.  They are dispossessed of all inheritance.  Their fathers have cheated on their wives, and their mistresses and son must then live in shame.

According to my notes:

The BASTARD: the dispossessed son, he burns with resentment. He can’t have what he wants, so he lashes out to hurt those around him. His deeds are often for effect – he wants to provoke action in others. He proudly announces his rebellious dealings. Don’t be fooled by his boyish demeanor – he’s a bundle of hate.