Twitter allows you to send a Direct Message to your followers and that message is sent to his Email or by SMS according to there settings. But its not possible to send a Direct Message (DM) to yourself via Twitter normal functions. But now there is an Twitter Web Application Privatetweet which can send private or direct message to yourself.

For a simple reason of storing a Tweet or anything else for that matter Privatetweet can help you send yourself 140 character message as usual by simply writing @YourTwitterID and you will receive a Direct message. Read more »