How do I get a remind for emails I sent that remain unanswered after a period of time?

While I've not (yet) used it myself, it looks like FollowUp comes close to providing what you're looking for. You can have it send you a reminder email just by adding the appropriate FollowUp email address to one of the addressee (to, cc, or bcc) fields of your outgoing email. If your recipient replies before your reminder comes in, you can cancel a reminder by either forwarding the message to the FollowUp cancel address or adding that cancel address as a cc/bcc if/when you reply to your customer. See the FollowUp Reminders page for more details.

Apparently, Boomerang for Gmail can do this: