If your Twitter account is sending DM spam, take the following steps:
1) Close Tweetdeck, Seesmic, Hootsuite or any cell apps that check your Twitter account.
2) Log into Twitter directly on the Web at http://twitter.com
3) Open “Settings” (It is on the top menu.) (Update: It’s now selected by clicking the menu pull down selected at the Twitter head & shoulders icon.)
4) See if you have a tab labeled “Connections.” (Update: the tab is now called “Apps.”) If so, click it and deauthorize everything you find there. If you want, note and reauthorize later.
5) Go to the “Password” tab and change your password. Make it longer and stronger.
6) Clear your Browser cache and exit.
7) Restart the browser and log back into Twitter.
Make sure you no longer have a “Connections” tab under settings. Update: Make sure you no longer have any Apps enabled. If you do, go back to step 3 and repeat.
8] If you use Tweetdeck, Hootsuite, Seesmic or other such third-party apps, you will need to give them the new password. I recommend you not do so for 24 hours. The fewer sites that have your password during this problem the better.
If someone you know is sending out Twitter spam, send them to this article.