What makes a website good is similar to what makes an interface good---and part of what makes a friend good.

It should be relatively stable (and so predictable, at least within limits). Newcomers need to be able to judge whether that particular site is worth their time.
It should be continually growing and changing so that visiting it once is not enough.
It should be large and diverse, full of interesting or useful information, helpful hints, images, downloadable software, or other things.
It should encourage the formation of a community of visitors by supporting whiteboards, chat, bulletin boards, graffiti, and so on. MUDs and MOOs, for example, are fun because you interact with other people as well as software.
It should be non-commercial (no annoying ads or other pitches).
It should be non-inquisitive (don't explicitly ask for visitor information). On the other hand, it should remember and adapt to the visitor's behavior patterns.
It should have well-organized and well-reviewed (and so trusted) links to other interesting places.
It should be a good viewing experience. It should use a minimum of different fonts and styles and have a uniform organization so that interaction quickly becomes predictable. The interaction mechanics should never get in the way of content delivery.
It should have short download times per page. If it has large pages they should be so marked, and they should be staged by smaller pages so that the visitor can get an idea of what they're about before going through all the trouble of downloading them.
It should tell its visitors something they didn't know before, or tell them something in an interesting way.
It should contain something startling or a new paradigm---a new way to think of something (for example, melt and X-eyes in X-windows).
It should let visitors leave their own markers and comments for new visitors to see. Visitors in MUDs, for example, can create new portions of the information space---that's one of the reasons they're so popular. This both empowers every visitor and also adds true complexity to the land.
It should look or behave differently depending on time of day. That sort of thing really serve to hammer home a sense of place.

What programs are fun to use?

X-eyes is fun because it follows the mouse (and so the user). It adds a feeling of interaction and paying attention to the user that other programs simply fail to do. It implicitly tells the user that he or she is important.

pad++ is good because it lets users overview the space if they want to without interrupting the metaphor (no stupid scrollbars), and hence without interrupting the smoothness of the interaction.

neko is good because it pushes the metaphor of the desktop one level further: if it really is a "place" then cats can play in it.

fish-eye views are good because they blow up currently interesting objects while still keeping their context on screen.

fish-cam and other webcameras are good because (1) they let the user control something and (2) they help to make the web a "place" and not a mass of formless data on some infinite disk.

--creating an animated face reflecting some information would be good; faces are easy to see and read and a face would help personify the interface.

--creating animated windows (windows that move around the screen on their own) would be cool. These Braitenberg windows should also be able to detect and respond to the user's actions.

--having animals roaming around windowspace (for example, birds roosting on each window) would be fun.

A browser popup window to show a webpage one link away. (No need to write a new browser: can put a link to your directory structure in your homepage so that you can click on it in the browser.) Recently visited pages should stick around when the current page is being viewed to give context for the current page. (This lack of direct display of recent pages is what makes it so very easy to get lost in webspace.)