Whether it's called a PM (Private Message) or DM (Direct Message), you have a red phone directly to you potential customer's desk.
But, before you start sending those private messages on all the great news you want to share, ask yourself if you're about to abuse that private line.
You wouldn't call the Kremlin to ask what they had for breakfast and you don't want to Direct Message a stranger to tell them about that great new investment opportunity or tool to help Facebook friends find them on Twitter. If you've sent more than a dozen cold DMs about your product/service, consider yourself the Social Media equivalent of a telemarketer.
Has the recipient been discussing the issue with you, or have they asked you about the topic? Then they've picked up that red phone and called *you* - jump on that opportunity as soon as you can. However, if you're sending out a message that is unasked for, unwanted, irrelevant or is being sent en masse then, when you look at your marketing tactic without delusion, you'll see that it's really spam and nothing more.
Every Private Message is a Privileged Message.
PMs should be relevant: There should be some previous sign of interest from the recipient
PMs should be authentic: Don't repeat the same message to multiple recipients
PMs should be targeted: Each consumer is different - show that you've listened and understood their point of view
PMs should be infrequent: This is a once-in-a-conversation opportunity. Don't hammer your followers of you'll find yourself blocked/ignored and possibly even reported.
Use your privilege wisely, and you'll not only enhance your current customer relationships, you'll create valuable new ones.