When should I use whom instead of who?

Formal:

   When who is the object of a verb, use whom:
      Whom did you see downtown?

   When who is the object of a preposition, use whom:
      To whom did you send the invitations?

Informal:

   When who is the object of a verb, use who:
      Who did you see downtown?

   When who is the object of a preposition placed at the end, use who:
      Who did you send the invitation to?

Both formal and informal:

   When who is the object of a preposition, use whom:
      To whom am I speaking?
      He is someone for whom I have great respect.
      To whom have you been talking?