Are you using a standard Kentico web part (repeater, data source, etc.)? If so, you can check the "Select only published" box in the web part properties.
If you are using a custom control, how are you getting your data? Custom query? Straight SQL?
Also, if you are logged in an editor and viewing the site in "Preview" mode, it will display unpublished items, as well. Be sure to click the "Close preview" link at the top of the page (when viewing the live site).