Two things that really bug me are images that have alt text when they shouldn't (ones that are purely decorative and don't add anything to the page) and ones that don't when they should.

The first is annoying, because when I'm using a text-only browser (which is most of the time, except at work) this type of image just clutters up the page. A common sub-case is having a blank alt attribute (alt="") which is presumably meant to hide the image from text-only browsers or screenreaders; I've added a hook in ELinks to filter these out.

The second is annoying, because these are images that I might want to see, but having no alt text makes this needlessly difficult.

A particularly egregious example is Wikipedia, where thumbnails have a blank alt, and so don't show up even though they're relevant to the content of the page, but the surrounding anchor element has the relevant description in its title attribute. What on earth!? Why does this make sense? Obviously the developers realise this information is useful, so they put it in the page, but not in the place where it would be most useful.

It's not a difficult concept: if an image is relevant to the content of the page, it needs a description in the alt attribute. If it's not relevant, it should probably be defined via CSS anyway, or left out altogether (either way, I won't see it).