As David pointed out, there should be some kind of alt attribute on every image tag for accessibility. It's intended to stand in as a text alternative to the image in the event the image isn't available to the visitor. This could be a visually impaired person or someone surfing with images turned off (text-based browser, slow Internet connection, PDA/cellphone, etc.).
Keep in mind that the search engine spiders are also "visually impaired visitors." They can't see any of the pretty pictures, either.
For instance, if the image is a link, I think the alt attribute should describe the destination of the link using words, in the same way that the image itself gives a visual indicator of where the link goes or what it does. The alt attribute takes the place of anchor text that you'd use for a text-based link.
So, just as you would try to have appropriately-keyworded anchor text on internal linking, you could aim for the same thing with the alt attributes of image links. As you say, not repetitious keyword-stuffed crap, but if you can write a relevant and useful alt attribute either using a keyphrase or without, why not write it with the keyphrase?
If the image is simply there as a decorative bit of eye candy, the alt attribute should still be there, but blank (alt=""). This allows speaking browsers to simply skip over the image, which is what you want to have happen for images that don't add to the meaning of the page content.
Of course, I realize from a copywriter's standpoint, that's the same thing as not having any alt attributes, because you generally don't really have to spend all that much time writing blanks.