Disco Elysium is one of the most engaging RPGs I've played in a long time. This is in large part due to its unique take on role-playing through social skills and an abundance of stat checks that influence the way you literally perceive and react to the world around you, but its quests played a significant role as well in hooking my interest from the very beginning and keeping me glued to my computer for the entirety of its 60-hour run time. The quests in Disco relate predominantly to your main investigation to solve a murder, with you playing a police detective waking up from a bad hangover, with no memory of himself or the world around him, who's been sent to figure how who killed the Hanged Man, and why, with two different sides on the verge of breaking out into violent conflict over the murder.
But throughout your time in Martinaise, you're able to get involved with numerous stereo investigations, or that is to say, side quests, most of which don't seem to be ostensibly related to the case or the greater situation in Martinaise, but which inevitably do wind up relating back to something important, somehow. The quests all contribute to a greater whole sum, in other words, which makes it a little difficult to pick out specific, individual quests since everything ultimately overlaps with something else in some significant way -- but despite that, I'm going to do my best to pick ones out that I particularly enjoyed, and go over what it was that made them so enjoyable. Additionally, I'll also expound on some that I didn't like as much, which is not to say that they were bad quests because I ultimately enjoyed just about everything in this game, but there were still a few that didn't live up to everything else, or that proved to be somewhat underwhelming.
As always, this is not meant to be an objective ranking of what quests have the most complex mechanics, or the best-told stories, or anything like that -- it's simply my personal opinion, on which quests I enjoyed most based on my own particular tastes and interests. Also please note that this article will have major spoilers for every quest mentioned, some of which will relate to important details in the main story, so just treat the entire thing as spoilers. And now, without further ado, here are my most and least favorite quests in Disco Elysium, in some attempt at a ranked order:

