Men at Arms, the first[1] book in Pratchett's City Watch subseries, makes for a wonderful introduction to the characters and world of Discworld. Admittedly, it's comparitively weak in some respects; like so many other series I've encountered, it suffers from "first book syndrome": weaker characterization, more predictable plot, and less elegant language. However, once you read it, you can get into the good stuff with an almost complete background of the characters. It can also be safely skipped in favour of Feet of Clay and Jingo, the next two books in the series. 
 The story takes place in the colorful, polluted, wild, cynical city-state of Anhk Morpork, cheerful center of crime of the civilized world. As Pratchett notes, 
 And visitors say: how does such a big city exist? What keeps it going? Since it's got a river you can chew, where does the drinking water come from? What is, in fact, the basis of its civic economy? How come it, against all probability, works? 
 Actually, visitors don't often say this. They usually say things like, "Which way to the, you know, the...er...you know, the young ladies, right?" 
 Ankh Morpork is ruled by the ascetic, incredibly crafty, and self-proclaimed tyrant, Lord Vetinari. Vetinari long ago decided that if the city was bound to have crime, it might as well be organized--so now the city is the proud home of the Assassins' and Thieves' Guilds, and people can buy yearly insurance against thievery (quite reasonable rates!). Since thieves do their own policing and punish non-guild members harshly (non-guild thievery is so bad for business), there's not much for Sam Vimes, head of the Night Watch, to do. Except, of course, get ready for his impending retirement and nuptuals to one of the richest women in the city. For a man whose entire life has revolved around his job, it's an increasingly terrifying prospect. And if that weren't enough, apparently his department has been chosen to herald political correctness by hiring a dwarf, a troll, and (oh, the horrors!), a woman. 
 But when a mysterious crime occurs right near the Assassin's Guild, Vimes' copper instincts are on fire. It's up to him and his loyal(ish) subordinates to ferret out the crime, all while the various guilds and the patrician himself seek to hold them back. 
 Men at Arms was my first introduction to Discworld, and, to tell the truth, I didn't warm to the characters when I first experienced them in this book. The narrative felt fragmented, as it's told from the perspectives of quite a large subset of the cast. While I loved Vimes, I felt rather mixed about some of the other characters-- in particular, Carrot Ironfoundersson, the Galahadesque white knight of the City Watch. I'm not entirely sure we're supposed to like him; I tend to identify with Vimes, who is himself rather bemused by Carrot. I find Carrot to be fascinating, for he highlights what I find as an innate conflict between taking the "right" and the "sympathetic" action. Carrot believes, at his core, that 
 "Personal isn't the same as important." 
 While I think all of us would admit the truth of this, and in the abstract, want the protagonist to take the action that protects the "important", the "greater good," over the "personal," I find the characters who do so to be unsympathetic, almost inhuman. Yet despite this, Carrot still manages to be oddly and universally liked. As one character puts it, 
 "Some people have inspired whole countries to great deeds because of the power of their vision. And so could he. Not because he dreams about marching hordes, or world domination, or an empire of a thousand years. Just because he thinks that everyone's really decent underneath and would get along just fine if only they made the effort, and he believes that so strongly it burns like a flame which is bigger than he is. He's got a dream and we're all part of it, so that it shapes the world around him. And the weird thing is that no one wants to disappoint him. It'd be like kicking the biggest puppy in the universe. It's a kind of magic." 
 The story is structured almost as a mystery, but not quite, as from the outset, segments are given from the perspective of the antagonist as well as the protagonist. The story utilizes a significant amount of dramatic irony; we know what the antagonist was doing, but have to watch our protagonists stumble around detecting. Notably, this is the last time that Pratchett employs this story structure; from here on out, the mysteries are mysterious to the reader as well as the characters. 
 For all that, the first time I read it, it kept me on the edge of my seat and up till 2AM to finish it. When I went on to read Feet of Clay, most of the characters really grew on me. This has become one of my absolute favorite series, and the pinnacle of it, Night Watch, is one of the best books I have ever read. Sam Vimes is, hands-down, my favorite noir/hardboiled/UF detective. Outwardly a Javert-like, rigid, rule-obsessed copper, he is also cynical, crafty, and incredibly soft-hearted. 
 Pratchett is, above all else, a satirist. He uses the nonthreatening and ridiculous world of Anhk Morpork to explore deeper philosophical issues. A few of my favourite quotes: 
 People ought to think for themselves... The problem is, people only think for themselves if you tell them to. 
 If you have to look along the shaft of an arrow from the wrong end, if a man has you entirely at his mercy, then hope like hell that man is an evil man. Because the evil like power, power over people, and they want to see you in fear. They want you to know you're going to die. So they'll talk. They'll gloat. They'll watch you squirm. They'll put off the moment of murder like another man will put off a good cigar. 
 So hope like hell your captor is an evil man. A good man will kill you with hardly a word. 
 Although less true in this book, most of the others in the series have provided serious food for thought in his nonjudgmental exploration of multiple facets of important political and ethical questions. Overall, the start of a great series. Worth reading if you if you want to get a full background on the characters. If you want to move straight to the best stuff, though, you can skip directly to Feet of Clay. 
 [1]I am potentially alone in considering this to be the start of the City Watch subseries of Pratchett's Discworld. Officially the start would be Guards! Guards!, because that is the first time the characters are introduced, but to me, there are so many differences in characterization between the Guards!Guards! version and the rest of the series, and so many retcons over the Guards!Guards! material, that I just don't consider it part of the series.