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: 
People don't read e-mails from bottom to top, and their attention is least likely to be on something that occurs at the end. If you want people to know, with the least amount of confusion or guesswork, do the work of writing a proper message with a proper subject line pertaining only to your change in status.

The footer approach will cause confusion - is that the impression you want? I think it'd be best to either be succinct, or don't send anything at all.
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.