I do remember those websites. For me, the difference is that now the Web is much more useful, but back then it was a lot more fun. True, you could sometimes waste hours following random links hoping to find something good, but the thrill of discovery when you stumbled across a gold mine of information was a huge part of the appeal. Nowadays, anyone with a basic understanding of search engines can find almost anything…
Browsing vs. searching. We don't seem to do much browsing anymore. We search and selectively pick what we consume. It's faster but, as you say, I don't think it is as fun. I used to enjoy picking a subject and then clicking all the DMOZ or Yahoo! links. I'd dig through webrings and and link aggregators with wild abandon. Now, I search a term and click on the first few results, at most. Sure, there are exceptions but…
I sometimes still do that with Wikipedia articles and their sources, it's a fun way to kill a couple of hours and can lead down some really interesting rabbit-holes.