ALT Tag is an ALT Attribute is an ALT Tag...
First, lets make it clear that although referred to more often than not as an ALT tag, an ALT tag is definately an ALT attribute not an ALT tag. In fact any html element placed within an html tag is called an html attribute.

Now, I'm sure we all know that an ALT attribute is the alternative text description for an image. ALT attributes display before an image is loaded and will display in lieu of an image if the image doesn't load properly, or if the image option is turned off within the browser. The ALT attribute will also display in text based browsers such as Lynx. According to the W3C, the ALT attribute is...

A required element for all images within a web page
Only to be used within image tags, nothing more
Specifically intended to describe only the image it is attached to, nothing more
Most visitors are likely to see (or hear) some version of your ALT text, so keep it meaningful, using ALT attributes only as they were intended.

ALT Attributes and Keyword Optimization
You should try and make your ALT text complete sentences, rather than simply a list of keywords or file names. Just keyword terms repeated over and over throughout a string of ALT attributes could actually be interpreted as spam and get you penalized by some search engines.

This of course does not mean that you should include the keywords within your ALT attributes that the page has been optimized for. Quite the contrary. By rights, any image included on a web page should by default be in context with the content and keyword terms being optimized for. Therefore, any realistic description of an image could certainly include some or all of the keywords being targeted by that page.

Benefits of Including ALT Attributes
ALT Text...

Enhances the browsing experience of visitors with disabilities.
Increases keyword density and relevancy for your targeted keywords and keyword terms.
Provides valuable information to visitors by providing descriptive text about images not being displayed.
Provides spider food for the search engines which helps them theme your pages appropriately when indexing.
ALT and TITLE attributes are both simple to add to your code, and remember that the ALT attribute is a required html element for images according to the W3C standard.

ALT and TITLE attributes boost your promotion efforts and your site's accessibility. ALT and Title attributes are a useful tool of optimization because the search engine spiders love the keywords so long as both attributes are used according to their intended purpose.

Visitors with images turned off or who use text browsers, screen readers and other assistive technologies, will appreciate your effort to orient them on your Web page and explain the images and the context in which they would appear.

There are few coding techniques that can give you as many benefits for so little effort as your ALT and TITLE attributes. Always include them and use them wisely!

ALT and TITLE Attributes from an Optimization Perspective
Use ALT attributes as they were intended, not simply as a repository for dumping keywords. The search engines won't like it if you do, and will reward you with poor search engine position or worse.

Use ALT attributes with all your Image tags (as per W3C standard) to describe the image or the image's intended purpose in the context of the web page and over all domain theme. Do it with keyword optimization in mind, remembering that the weight given to any one particular ALT or TITLE attribute is probably miniscule at best, yet when combined to carrry your keywords and theme domain wide can make a real difference for both your search engine placment and the user's experience while navigating your site.

ALT Attributes and the Search Engines
In the webmaster help sections for virtually every search engine, they state that you should use ALT text to include additional keywords. The problem with this broad statement is that many of the unethical and rookie seo companies, have spammed the search engines using both ALT and TITLE attributes, as well as ABBR and others, often using a simple 'find and replace' technique to dump the same keyword terms into all the ALT and TITLE attributes within a particular page. This is bad seo practice and will do nothing but hurt you in the end.

The ALT attribute and the TITLE attributes are for two distinctly different purposes, and should contain descriptive text that makes sense, is meaningful, adds value and purpose to your web page, and contains keywords and keyword terms specific for that page and/or the domain (domain wide keywords and terms).

Research has yet to find any solid evidence that any of the search engines actually use the TITLE attribute, but all do use the ALT attribute.

Last Word on ALT Attributes and Search Engine Ranking
It's unlikely that any one single TITLE or ALT attribute can directly alter your search engine ranking in any meaningful way. However, when used thoughtfully and as intended throughout a web page, or better yet throughout the entire domain, the TITLE and ALT attribute can make a difference, a difference you can take to the bank.

Modern search engines are so sophisticated that when you make the effort to improve your websites usability and the value it offers your visitors, it begins to stand out from the crowd. Suddenly the search engines recognize your site as a website with purpose and value, and begin to reward you accordingly.

The extra time you spend developing and writing effective ALT and TITLE attributes will bring rewards in the form of better search engine position and ranking, a reward well worth the effort!