I noticed that some people forget to respond to an e-mail for weeks. Usually, it's because of either poor inbox management (read not following Inbox 0 rules) or simply overwhelming number of messages. Well, if you send plenty of e-mails it becomes tough to keep track of the ones sent weeks ago especially when it the subject isn't urgent.
The old school way would be to go into your Sent Items and look for the message. If you use Google Mail, the task might be easier as each conversation takes only one line regardless of the number of messages involved. However, if you are using any other mail client it becomes a nightmare as you sift through dozens of unrelated messages. Here's a solution: mark all of your outgoing messages for quick review & remove the mark once a reply is received. (This is a relatively known “hack” among GTD practitioners.)
In GMail, you can create a filter for all messages from you and apply a label, say “Waiting for.” To do this, click on “Create a filter” to the right of the search field, enter your e-mail address into the “From:” field, go to the “Next Step,” and select to “Apply the label.”
In other e-mail clients, open your rules dialogue window, mark the condition as the “From” field with your e-mail address in it, assign a category (color or label, whichever your client offers), and finish the prompts.
I suggest you review the content of the assigned label or category every morning to see the statuses. If you reasonable waiting time has passed, simply make a to-do item in your favorite task manager to follow up. If a reply has been received, act on it accordingly.