Links sections were awesome, and made the web feel deeper than it really was. You could go on dives just clicking through and finding so much cool stuff. Plus if it was a hobby site, there was inherently some level of curation - I don't think anybody would be linking to any of the hundreds of lookalike SEO "blogs" nowadays if it weren't for search engines allowing themselves to be gamed.
Nowadays if it's not on the first "page" of Google (well, whatever the first group of infinite scrolling results is called) it might as well not exist. Makes the web feel flatter and less like a, well, web.
Webrings and some called them "Affiliates" (I dont know where the name came from, it makes more sense in Spanish, not sure in English), but they had this 82x32 buttons on the sidebar (sometimes anitmated GIFs) to similar websites, usually websites handled by friends.
+ the webrings.