It supports, but does not overpower, the message. It is appropriate to the particular message being conveyed. A basic principle of classical aesthetics is that a good piece of art has a balance of unity and variety. That is, everything fits together into a recognizable whole, but at the same time there is enough variety to keep things interesting.
Most Web designers err on the side of too much variety.
The design of a site needs to be consistent from one page to the next. No matter where someone is on your site, they should know that they're on your site and nobody else's. One of the central elements of your brand is your logo. Choose a logo carefully, and whatever file formats it exists in, make sure that the files are top quality. Once you choose a logo, stick with it and use it throughout your site.