It could be beauty, enjoyment, entertainment. But for many of us the only real goal is to convert a user.
On the eCommerce projects I've worked on, a "conversion" was defined as a user simply making a purchase. So the goal of any of our designs was to make that action happen as often as possible (in as high quantities as possible). At the end of the day, it didn't matter if we personally hated a design, or if we thought it was ugly or anything like that. The design that made the most money was the best design.
Ultimately, it is for conversion of the right person. Conversion may mean anything from giving your existing customer information they need, getting a new customer on board or getting a newsletter sign up.
Now that task could be range from buying a faucet to seeing when your favorite band is in town. The easier it is to accomplish the task, the better the website.
But what about making a site that's pleasant to use. It might take more clicks to get somewhere but the style and experience is better. Sites like HN and the Drudge Report convey the information effectively but they are not necessarily as pleasant to use. Is designing a site like designing clothes? If so, function is definitely not the only consideration.
Design will always be a blend of form and function. With an optimal goal of creating a product that is aesthetically pleasing and easy to use.
I would error on the side of making something more useable than beautiful. If something is ugly, but still usable, it has value. If something looks good and is not usable, it doesn't have much value. Unless it's Art or something that is only meant to be looked upon.
On the eCommerce projects I've worked on, a "conversion" was defined as a user simply making a purchase. So the goal of any of our designs was to make that action happen as often as possible (in as high quantities as possible). At the end of the day, it didn't matter if we personally hated a design, or if we thought it was ugly or anything like that. The design that made the most money was the best design.