Me and other developers at our company are struggling with "title" and "alt" attributes. In the past, we added "title"-Tags to all links for SEO purposes (although some of them were annoing talking about usability) and "alt"-Tags on every image on the site, because HTML4 spec said so.
Check the HTML specification to see what is/isn’t required:
a
element: The (global) title
attribute is not required.
img
element: The alt
attribute is required in most cases (exceptions).
(Questions about the SEO effect are off-topic on Stack Overflow. They can be asked on Webmasters SE.)