Messenger Plus! Live Chat Logs
In Messenger Plus! Live Preferences & Options:
- Click the "Conversation" tab along the top
 - Click the "Chat Logging" tab on the left
 - Ensure that Enable chat logging by default is unchecked
 
Windows Live Messenger Chat Logs
In Windows Live Messenger options:
- Click the "Messages" tab on the left
 - Look for "Message History" 3/4 of the way down
 - Ensure that Automatically keep a history of my conversations is unchecked
 
 Also, please search the forums as this question has been answered numerous times before, not least by myself just a week ago