In my personal opinion a 100% answer is up in the air. I do believe they help to a point, but not to extreme measures. Two things I consider regarding alt tags are universal search results and usability. Adding an alt attribute can increase chances of having it listed within universal search results and also provide a short description of the picture for users. Well, Search Engine Roundtable conducted a survey asking SEO professionals whether or not alt tags improve search ranking and 80% of the respondents say 'yes' and 20% 'no'. I guess I am not surprised by the results, but would have thought the 80% would have been slightly higher. We can't agree on everything, right?
Alt attributes are an easy add to an image that is often overlooked before an SEO professional gets their hands on it. Because it so easy to add, use them! Most people agree that meta keywords carry little/no weight in search engine rank, but we still use them. Why? They are an easy add...and who knows, they may carry just enough weight to give a small boost.