It may not sound that critical factor if you think about your website's rankings in Google's search results but real picture says a different story.
Recently, a website owner witnessed a steep (63%) decline in his site's ranking after he made some design changes to his site.
You can read about his problem here on Google forums.
One of the Google employee on the forum made an interesting observation after visiting his website code is that the website's images contained alt tags which were populated with long texts or sometimes the web page's title text was itself copied into all images on that web page.
It is not certain that these long texts are the cause of his site's reduced rankings or it is something else like the panda update of Google's algorithms but the long texts and unnecessary words in the alt attribute are not good for SEO.
Here are some guidelines on how to use appropriate text in alt attribute.
Lets assume that you have an image of a puppy on your web page, then following scenarios may happen:
Bad:
<img src="puppy.jpg" alt=""/>
Having no text in alt attribute is the worst thing. Many people-for example, users with visual impairments, or people using screen readers or who have low-bandwidth connections-may not be able to see images on web pages. Descriptive alt text provides these users with important information.
Better:
<img src="puppy.jpg" alt="puppy"/>
As a popular proverb says: Something is better than nothing!! So, this works if you can't think of any better text.
Best:
<img src="puppy.jpg" alt="Dalmatian puppy playing fetch">
This is the best text as it helps both the text browsers, visually impaired users and search engines to know what the image is all about.
Worst:
<img src="puppy.jpg" alt="puppy dog baby
dog pup pups puppies doggies pups litter puppies dog retriever
labrador wolfhound setter pointer puppy jack russell terrier
puppies dog food cheap dogfood puppy food"/>
This is really bad as you are only trying to stuff your web page's keywords instead of explaining the image. Search engines do not like this and neither would it help visually impaired users.
Here is a video from Matt Cutts (Google) on how to create an effective alt attribute for an image:
Moral of the story
Keep it "To The point" :)