The design of a website itself is seldom the main attraction -- at least unless it's a website on design. Few such sites exist.

The website should be focused on the content itself. The design should be as minimal as possible. This said, there are certain justifications for design:

• Give your site personality.
  A site usually consists of several pages. The concept of site is really just an abstraction on this. Yes, all the pages probably exist on the same server, and the URLs look similar -- but no one will notice those details. What they will notice is a common look across your pages.
      To get this common look you can use a logo, a color scheme, and a common layout. More than that is unnecessary -- don't use clever animations, text made with images (used to get just the right font), splash screens (a contentless intro screen), or any tricks on the user (like never linking offsite, or having offsite links open in a new browser).
• Express your role in the web.
  Without even reading any text, it is usually possible to figure out what sort of organization you are looking at in a website. Is it a personal site, an organization's site, a corporate site? Details in color and layout present a feeling, just like you can tell the difference between a Daniel Steele and a Toni Morrison novel just by looking at the cover from 5 feet away. You should be able to do the same with the website.

With that said, there are some justifications for design that I think are not really justified:

• Use a design like site X.
  When given alternative designs, people will often gravitate to some design they associate with success, even though it isn't appropriate, or just simply isn't good design. Most large corporate websites have a design that reflects a considerable amount of content, very active maintenance, and a sort of flashy design that just isn't necessary.
• Design should look cool -- just like you.
  Oh, whatever. Unless you are in graphic design, the design of your site is not the point.
• More is better.
  Maybe you can make a little money by putting an ad on your site (wishful thinking). Or sign up to a couple web rings. Or maybe just a link exchange. It's tempting... but there's nothing that taints a good design like obnoxious icons and logos, and doubly (nay, five times) worse when they are animated. Such things are deliberately distracting, specially designed to attract your viewers' attention at your sites expense. (Web rings have a certain democratic nobility, and try to be truly helpful. Unfortunately, they have an amateurish feel, and aren't very reliable.)