On average, I send about three emails a day to people I may have never emailed before, or have but don't see regularly. In both cases I forget that I've emailed them, so if they don't reply then the conversation is 'lost' forever.
My ideal solution: I know Gmail stores the message, but I want some kind of added notification system, or dashboard, or report that says "Hey, in the last 5 days you sent out 20 emails that still haven't been replied to yet." And I can see which ones still haven't been replied to and then re-send a message.
Best Answer
Apply a label to the message you send (e.g., "Waiting for Reply"). Then you can check that folder every few days to see which messages have been responded to and remove the label as appropriate.
I use a filter to look for a specific string in the body of the message to automate adding the label.