Some of these are userscripts, for which you need Greasemonkey (Firefox) or Tampermonkey (Chrome or Opera).
AO3 Crossover Savior - For hiding stories with too many fandoms from the search pages.
AO3 Lazier - Adds a button to take you to the latest posted chapter
AO3:Kudosed and seen history - for those of us who forget whether we've read a story before - show the ones you've given kudos to or marked as seen.
AO3 Saved Filters - a way to apply a specific filter every time you search on the archive, so you can block stories from a specific fandom, or with a specific pairing. It combines very well with...
"The "Search Within Results" Field and You" - instructions on how to rule items out of searches, using the internal number codes for certain tags - fandoms, pairings or characters.
Something else I went looking for was a way of loading stories without the collections they are part of, as I'm picky enough to want all my bookmarks to look the same. I asked over at the dreamwidth AO3 community and somebody made this bookmarklet.
So, if there's any particular function you want to know about, it's worth looking there, at ao3some or at all the userscripts people have written for the archive.