An e-mail containing a time-sensitive question for which you are awaiting a response. When such an e-mail is sitting in one's inbox, they are said to have a 'hangmail'.
1: "You've got a hangmail."
2: (via SMS) "BTW I asked you to marry me through e-mail. Can you at least confirm that it went through? I hate hangmail."
A - "You've got a hangmail on your finger."
B - "I think you mean hangnail."
A - "Oh ya."