In general, I believe, a "good" design is one that supports the purpose of the web site. Thus, there's no general answer. It simply depends on the purpose.
However, there are some elements that every web page has or should have in one form or another:
Call To Action
The most importent element. You want your users to do something, so you must tell them what to do. What it is depends on your web site or product. There may be several calls-to-action, and a series of them is often called a (sales) funnel.
In general, the less steps necessary to complete an action, the better.
Everything that enables the visitor to do something: Forms, buttons and other widgets. Their purpose should be obvious.
This is used to describe the benefit or utility of the product, establish a certain emotional mood, provide information about your product, and -- most importantly -- answer ANY objection visitors may have NOT to act on the call-of-action.
The most common objection is risk-awareness or uncertainty: Will following the call-to-action really provide the promised benefit? Typical solutions include guarantees, testimonials, free trials, etc.
There are basically two camps with different ideas what headlines should do. The first ones assumes the purpose of headlines is to describe the product and/or its main selling point. The second camp assumes their purpose is to make the visitor read the first sentence of the copy. These are not mutually exclusive, so one may find a headline which does both, sort of.
Depending on the camp, sub-headlines are then either used to structure the copy or to provide additional entry points to read the copy, respectively.
Often over-emphasized, but sometimes useful. It includes logos, CSS design, images and video. Graphics is good to improve recall or recognition, to establish an emotional mood or atmosphere, and to add credibility.
Sometimes, it's also used to suggest additional benefits that are either hard to describe in the copy, or that you don't want to describe, at all. (Think, for example, the fetching girl in a car ad).
Graphic is also relevant when leading the visitor's attention, thus graphics should emphasize the important elements, usually the calls-to-action and the headlines.
On top of my head, that's it. Basically.
Hope this helps.