In the past years of browsing the internet and visiting the websites of artists, I have come to realise they can be roughly split up into four categories. Please note that these are not absolute and there are definitely exceptions to everything I'll say here.
The first category I would call the website of the young artist. The website of artists at an early stage in their career is usually marked by a significant lack of personal knowledge on website design, as well as funding to hire somebody who does. The main purpose of these websites is to be a showcase of the persons work, as well as allowing people to retrieve some kind of contact information.
In order to nevertheless provide the visitor with a professional-looking homepage, their lack of resources is most often compensated by free frameworks such as indexhibit. While these are functional, they often result in websites that appear commonplace with code that is difficult to read.
Examples include Wesley Meuris, Chaim van Luit, Katja Mater and many others.
When artists have a bit more options at their disposal, it seems that their websites change accordingly. These websites are often not that much more complicated than those of their younger colleagues, yet much more attention has been given to details that distinguish them from others with a more generic appearance.
The website of gerlach en koop is a great example. Its very straightforward, yet every detail has been carefully considered. There is a interesting day/night mechanic and the various clickable projects are separated by a simple yet effective forward slash. This forward slash is also featured as the websites icon, that together with he somewhat unusual url help it stand out. The font used is Frutiger, noted for its legibility, and although widely used, it helps to differentiate from the ubiquitous instances of Helvetica.
Another good example is the website of Cory Arcangel. At first sight it might look like a typical early 2000's style blog and therefore at odds with Arcangels often technology-focused work. In reality this kind of website is quite typical for technical people. People like Jonathan Blow and Neil Sloane have extremely bare-bones websites where the appearance of the code has been given more attention than the GUI. This can also be seen in the website of Arcangel, with code that is properly indented, aptly characterised with comments and exceeding the width of the screen only when necessary.
Further examples of this kind of website include Philip Metten, Gabriel Lester, and John Körmeling. Each of their websites accurately resemble their respective practices even at first glance.
In all the previously mentioned websites contact information still plays an important part. Even in the case of Cory Arcangel, whose career must keep him rather busy, an email address for his studio is still provided for feedback on his undertakings.
For those artists to whom interaction with the general public is unwanted and who can afford to miss smaller opportunities, the ultimate attainable goal is to have no website at all. These artists are instead represented on the world wide web by their galleries, so that valuable information can be controlled and business can be conducted according to established contracts, while the artist is left in peace.
A slightly less aloof alternative to this practice is a website where nothing but a link to those galleries is presented, as is the case with Tacita Dean, Elmgreen&Dragset, and Heimo Zobernig.
Then there are the websites of those artists who have nothing to prove and posses more than ample means to maintain them. These websites tend to serve as a public archive. Martin Creed, Bernard Frize, Damien Hirst, Thomas Schütte, Anthony Gormly and Gerhard Richter all provide the visitor with a detailed overview of their long careers.
As a final note there is one more category of artist website. Usually these are of deceased artists, whose estate is now managed by a foundation that is set on publishing a catalogue raisonné. Helen Frankenthaler, Donald Judd, Anne Truitt, and Roy Lichtenstein are but a few whose work has been poorly kept track of during their lifetime and now are appealing to the public to send them any information they may posses.