You've probably seen one or another of the various maps of the Internet, the ones that look like a cross between a galaxy and a spider's web? If not, check the link below for a colourful example, and the second link for some more.
Mapping the whole Internet is a bit of a tricky project, but an altogether
simpler task (says he, the non-programmer) would be for your web browser to create and update a personal map of 'your Surfiverse' based on your browsing history, showing the websites you've visited.
Webpages would appear as nodes, links as links (well, duh). The map could be coloured in several ways: for example, recentness of last visit to that address, number of visits to or length of time spent at that webpage, geographic location of website, and so on.
Ideally you'd be able to use this map for navigation - zooming in on a particular area to see more detail, pointing your mouse arrow at a node to see its URL, and clicking on the node to go to that webpage. More fun than just selecting a bookmark - with this you really feel you're journeying through cyberspace!*
But even aside from its usefulness for navigation, it would just be pretty and interesting to look at. And it might encourage people to widen their browsing habits to expand their Surfiverse, rather than sticking to the same few sites every time.
"Wow, what's that massive, white-hot star in the centre of your Surfiverse? You must visit that site a lot!"
"Um, that's the Halfbakery..."
*Reality described is a serving suggestion only. Your reality may differ from illustration.