When a message is sent, the sender is prompted with a "Track / Don't track" option via a simple UI pop-up. Alternatively this could be a tick-box on the compose UI (however people may forget to tick it), or a prompt only for a pre-defined list of contacts (regular late-response offenders), or a prompt if the destination email address has been tracked before, or a prompt only if the email contains particular wording (e.g. making a request) (semantic analysis required).
A UI screen would be required to view all messages currently being tracked (and history).
When the user receives a response to a tracked message, they prompted to remove from tracking list (e.g. if the required information has been provided).
A possible extension of this functionality would be an option to track an action for each recipient.
Why not use Outlook task functionality? It's too formal and too demanding (it creates the task at the destination end, not the sender end). Plus its Microsoft...