If you have used Twitter direct messages frequently, then you might have lots of DMs in your inbox, but Twitter does not offer any interface to delete multiple DMs or DMs from a particular user. InboxCleaner is a nice online service which allows you to manage direct messages in Twitter. You can log into Twitter using oAuth and then the service fetches all the DMs in your account.
Once logged in, the service displays all the DMs in your account. You can either delete all the messages in one go or delete messages from a particular user alone.
InboxCleaner is a very simple online service to clean up your messages in Twitter.