If your Twitter name is suddenly tweeting spam or sending DM spam, your account has been compromised in some way.
This is usually due to your having authorized some unscrupulous App vendor, either by entering your password, or simply "allowing" it to connect to your account via Twitter's oAuth system.
The Fix
- Change your password immediately.
- Go to Twitter.com > Settings > Connection — Revoke access to anything you don't need or recognize.
It's not a bad idea to kill them all, and reauthorize each as you need them. In many cases, you'll never revisit many of them. Most of the major services will be safe, but there are so many Apps now, many will not be. One of them is the one using your account. This will fix it.
Prevention
Don't be too quick to authorize an App. Ask yourself, "is this really worthwhile, or just some stupid game or gimmick that really isn't worth the hassle if it's malware."
But don't be too paranoid, either. Many Apps are fun and useful, and most of the time the compromising is just a mild annoyance, but not harmful enough to really worry about.
When Your Twitter Account Gets Hacked