When it comes to all forms of design and art, the general rule is to keep it simple. Writers are told to "Kill your Darlings" and self-conscious girls are told that "Simplicity is Beauty" Web designers and logo designers on the other hand are given the saying "Keep it Simple, Stupid"
However contrary to popular belief, it's actually much more difficult to make things simpler than to complicate things. Let's take for example a blank blue box. It is a lot easier to fill that blue little box with text, images, brushes and patterns than to think of a single pattern or a single text or a single image that would translate everything you want to say in one fell swoop.
Simple designs can sometimes be alternated with minimalistic and there's nothing wrong with that. However simplicity is not about cutting everything off, it's about balance. Excluding a lot of functionality in a website can prove to be appealing to the eye but users would curse while trying to decipher where the damn "sign up" link is. As with fashion and with any fashion trend, there is also what we call a Fashion Victim.
Smash Magazine has a list of simple web designs that can be a good model for web designers aiming for that balanced, simple look. My favorite is this:
What I like about this design aside from its colors is its usability. The eyes move downward and the information flows.