The question of what is and what is not art has been a hotly contested question for hundreds of years. A particular group of people may consider something art while another group members it junk, or are even offended by the information that something could be considered art. There have been numerous art movements throughout history that when they first appeared the critics of the time scoffed at the perception of that art movement being considered art. But generally the movement that is at first not considered art, is ever accepted.
I think this is because people love the art on the fringe. They love art that pushes boundaries and breaks the rules and says new and interesting things in new ways. Think about the best-known artists through history and what they are known for. They are known for being new and innovative, for going places in art no one has ever been. Picasso was known for his abstraction of the human form, despite the fact he was a master skill level artist of plain realistic reproduction by the time he was 16. Jackson Polluck was known for being one of the largest names in Abstract Expressionism, a movement that broke all the rules in traditional painting.
As the times change the media of new art also evolves. There have been numerous changes in this area in recent history. With the video revolution, art also took up video as a media that could be used artistically. In fact artistically animated movies were some of the first video to be produced before a feature length film was released.
So anyway, back to the topic of web design. I think if you asked your average person if web design was art, they would be unsure as to what to respond. I myself had the same response. I believe this is because of the fact that most websites you and I use from day to day do not have art in mind as the primary component.
They probably have some graphics related to the website content, and some nice pictures of happy customers, but when they were building the graphics for the website they did not particularly give much thought to the meaning or many other things an artist would consider while creating a piece. In short, most websites that the average user visits regularly are probably designed for functionality; they were designed to be efficient and convey a message properly.
But this is not to say web design can not be art. As with any medium, the artistically motivated will mold it to fit their desires. The capacity for something to be art is almost limitless; all that is required is the motive and the reasoning for something to be identified as art. Websites that are a little more off the beat path for the average user is where you will find artistically driven design.
This is not to say that art has to be the chief component in any commercial website; functionality should be, which is why you find sites designed by it so often. But the point is that art in any given website should be given more thought.
A successful integration of art, design, and functionality can make a site be far more successful in the long run. With the obvious help of your site looking professional and polished, good art integration can subconsciously move the eye around the page to key points of interest, it can keep visitors longer, and it is a testament to the quality of your message.
A couple websites worth checking out that are resources for art heavy designs would be:
These sites are just the tip of the iceberg as far as what is out there; you just have to look, step outside your normal internet box onto the innovating design area.