If you don't know about the email processor, briefly it's a way to file emails into CiviCRM as activities, and less briefly, see http://book.civicrm.org/user/current/advanced-configuration/email-system... (about half way down).
I've been doing some fiddling with drag and drop and, in particular for CiviCase, it would simplify the process of getting the emails into CiviCRM. It also removes the need, if you're using the IMAP method, for storing everyone's individual email passwords in the CiviCRM admin page settings. And it would work with attachments.
One possibly big drawback is it would only work in native email programs, like Outlook, Thunderbird, etc. It will NOT work when viewing your email via webmail/browser, but I think there's a big enough pool of people and organizations who use native email programs that this could be worth it.
Currently for CiviCase it's a multistep process, where you have to first use the email processor, then wait until cron does its thing, then go find the email in CiviCRM, then choose File On Case. My goal is you could just drag the email from the inbox into an open CiviCRM browser window, fill out some info in a popup box, and then you're done. Ideally, if you already had a Manage Case screen open, it would default to that case.
I don't have anything actually coded yet, so I'm mostly posting this to gauge interest and to see if anyone has maybe already done something like this or is interested in helping.