In Sharepoint 2007 you have a great permission you can set: 'Only their own'. This allows someone to view and edit only the items that they have created, and not other items that other people have created. Administrators of the site can see everything, of course.
This is easy to set on a List under the list settings. However, if you are using a Document Library, the setting is nowhere to be found. It is there, but it's hidden.
To change this setting, you can either write some code, as described here, or you can do the equivalent with Sharepoint Manager (make sure you get the 2007 version). Open Sharepoint Manager (while logged into your Sharepoint Server), drill down to the Document Library you are interested in, and you should see the 'WriteSecurity' setting. Change it to 2 to effectively set it to 'only their own.'
However, keep in mind that this only changes what the user can do via the UI. If they get to the list data via web services or some other method, this won't prevent them from getting at other people's data.