After you wonder on some mystical, lovable, creative web designs in the internet, you might want to just review the basics of visual design. Start with the principles of design, they do also apply to web design, such as, Balance, Proportion, Rhythm, Emphasis, Unity. I guess these terms do speak for themselves, but if you still can't get it, you don't have to look far, just look at your face.
Normally, we have sets of eyes, ears, nosetrils... the left mirrors the right. In short, there's the Balance. Now depending on the sizes of these parts can make you beautiful or ugly, we call that Proportion. When a beautiful face, or any face just smiled at you, notice how the lips, eyes, cheeks, eyebrows,... just start to move in harmony, yes... you bet, that's Rhythm. There's always the one thing that's noticeable about one's face, whether his/her set of eyes, nose, lips... probably big or nice to look at... we call that Emphasis in design. Eyes, nose, lips, ears, cheeks, etc. are all placed on one's head, somewhat grouped by purpose... Unity, united to form a head.
So, I should say that a very principled head can be very attractive.
When designing a website, you have other reasons to place a mirror beside your computer aside from vanity, better yet, place a portrait of someone you admire for beauty, that's if she/he ain't you.
What kind of design?
Design should follow the concept. It should help to clarify the ideas or make the messages felt by the viewers... it's like setting the mood.
You don't need to put lots of images, colors just because others are doing it. If it doesn't help clarifying or these elements are unrelated to the concept, better not add them.
You don't need to put lots of visual effects, animation just because you know how to or just to impress your visitors. If it doesn't simplify navigation of the site, it's an awful way of wasting your visitors' time, and computer processing time.