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.
I don't see any problem with using the signature function of your email client to automatically append a note to the end of all of your emails explaining that you will be leaving the company. 

I wouldn't make it *look* like a signature, but in all the email clients I have used the "signature" is just text added to the end of the email. Just add the note above your current signature.