Question: I have given notice at my current company and have admittedly done a poor job of organizing all of my contacts, so sending out an email to all of them would be tedious to say the least. Everyone internally knows of my departure, it is the people outside of my organization that I am concerned about.

Would it be generally appropriate to include the fact that I will no longer be with my current company in my email signature? I feel that giving this notice to everyone will cause a lot less headaches for them down the road.

Is it even my responsibility to inform them that I am leaving? (I have no problems doing so)

I also plan on setting up my out-of-office reply to include this information once I leave to handle any overlap between incoming emails and my company shutting down my accounts. Is this appropriate as well?

Note: Everyone internally knows of my departure.

Answer: 
Issues of professionalism or appropriateness aside, using your email signature to announce your departure is likely to be *ineffective*. The vast majority of email clients de-emphasize or hide signatures by default, so most of the people you're trying to contact with this method will never see it.
The customers your company has after you leave are of little concern to you, to be honest. If they want to keep them, they will contact them and let them know that another person will be handling their accounts. Unless you're expecting to keep up with the customers after you leave for some other reason (which would be unprofessional if you keep to the same industry), then you leave the company and let the company deal with **their** customers. Personally, I don't want the clients I work with to know when I'm gone.