All images in the HTML should include the ALT attribute to be valid HTML and aid assistive technologies and for users browsing without images. However all background images and decoration must be moved into the CSS and therefore there is no IMG tag to need to apply an ALT attribute.
1.
If decoration images must be in the HTML then a blank ALT attribute should be used. (ideally should have used CSS).
2. If the content of images are links then an ALT description is legal requirement and will help SEO.
3. If the content of the images is descriptive like a diagram or photograph you should describe it in the ALT text sufficiently to inform a blind user.
For more information: If you are in the USA please read Section 508
www.section508.gov and in Europe/Australia please read WAI by W3C
www.w3.org/WAI