Yes, the image should be descriptive of the image and, if it is a link, where it is taking the visitor. However, since images used should be relevant as well as links, a descriptive alt/title tag using relevant keywords would be in order.

If you start using such tags with keywords for border graphics and the like, then that is not recommended. Simply use the alt="" to make the image validate. Also, if the alt/title tag looks like "spam spam spam and more spam", then you are over doing it. Just use common sense and you'll be fine.

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