The Discworld Companion

Ankh-Morpork (excerpt)
Over the millennia the city has tried various forms of government; an ancient system of sewers - known only to the Assassins' guild (until Men At Arms) - and a few other details testify to a glorious past (glorious being defined as a time when Thousands of People Could Be Persuaded by Men with Swords to Build Big Things out of Stone).There has been monarchy, oligarchy, anarchy, and dictatorship. The current system appears to be a sort of highly specialized democracy; as they say in Ankh-Morpork, it's a case of One Man, One Vote - Lord Vetinari is the Man, he has the Vote.
In essence the city is governed as a result of the interplay of various pressure groups. Lord Vetinari positively encouraged the growth of the Guilds, of which there are now some 300 in the city. His reason for doing this may be discerned in his unpublished book The Servant, a compendium of advice and precepts to a young man setting out to govern a fictional city (in the book identified only as AM), in a passage which runs: 'Where here are clearly two sides to a question, make haste to see that these rapidly become two hundred.' In practise, the city's political structure consists entirely of a huge number of pressure groups plotting, fighting, conniving, forming alliances, shouting, scheming, intriguing, and making plans, in the middle of which one man in quietly doing things his way.

Laws of Ankh-Morpork (excerpts)
There aren't any.
Well…
Not entirely true. There aren't any now, except in the almost iconographic memory of Captain Carrot of the city Watch. There are Guild laws, administered by the various Guilds and often the cause of friction between them (see Vetinari, Lord), but laws in the modern sense have gone out of fashion in the last several hundred years. The city is not, however, lawless. It more or less runs on the 'Patrician's Rules'. Lord Vetinari takes the unvoiced vow that most citizens are guilty of something , or just generally guilty in a low-grade way. If there is a crime, then there ought to be seen to be a punishment; if the punishment can involve the actual perpetrator of the crime then this is a happy state of affairs, but it is not essential. Anything that threatens the city in any way - be it a man, a philosophy or a device - is 'against the law'.
Beyond that, Lord Vetinari believes in a common or natural law; if a man can sell short-weight bread and get away with it, then get away with it he does. If, however, his defrauded customers decide to nail him to his own ceiling, then that is fine, too.
[…]
Although the current system in Ankh-Morpork consists almost entirely of 'Guild Justice' enforced by the city's Guilds, it is still the case that criminals taken by the Watch may opt to stand for trail before the Patrician.
The accused may, if they have money, employ a member of the Guild of Lawyers (motto: LVCRE SERMAT [Money Talks]) to speak on their behalf. If they wish to be found not guilty they will often need large reserves of money. The long-held principle is very clear - the more money you have, the more likely you are to be innocent. This is considered right and proper by the Guild, because rich people are an asset to society and there are far too many poor people poor people around in any case, and they're probably all criminals.
If the accused has no money, then their only hope is if the Patrician decides in their favour. He quite often does so, because he finds it instructive to all concerned.
[…]
The death penalty is usually reserved for treachery to the city, continuing to commit murder after being told not to, irredeemable stupidity while not being a troll, and persistent street theatre.

Monarchy, Ankh-Morporkian (excerpt)
And so the rule of kings gave way to the rule of Patricians. In a kind of mirror image of democracy, they have tended to get into power by lies, trickery and deceit, but remain in power only by a very crude democratic process; if they make too many enemies, they'll be out of office, power, and probably their corporeal form. It seems to have worked, possibly for the reason advanced by the current Patrician in his treatise on the art of government, The Servant: 'If it continues for long enough, even a reign of terror may become a fondly remembered period. People believe they want justice and wise government but, in fact, what they really want is an assurance that tomorrow will be very much like today.'

Patrician, Office of.
The Patrician is the ruler of Ankh-Morpork. There have been no monarchs in Ankh-Morpork for 300 years, since the death of the last and possibly nastiest (see Lorenzo the Kind). The only real qualification to rule in Ankh-Morpork is the ability to stay alive for more than five minutes, because the great merchant families of Ankh have been ruling the city as kings or Patricians for the last twenty centuries and are as about to relinquish power as the average limpet is to let go of its rock. Past Patricians have included:

Hogarth, Frenzied Earl [GG]
Harmoni, Deranged Lord [MAA]
Nersch the Lunatic [GG]
Olaf Quimby II
Scapula, Laughing Lord [MAA]
Smince, Lord [GG]
Snapcase, Mad/Psychoneurotic Lord [GG, MAA]
Winder, Homicidal Lord [MAA]

Patrician, the (Lord Havelock Vetinari).
Age uncertain. Background unavailable. Reputedly trained at the Assassins' Guild school. Now supreme ruler of the city of Ankh-Morpork, to which he is totally devoted. Tall, think, and generally to be seen wearing black.
He is the most recent of a line of unelected heads (see above). As their names suggest, these were not wholly pleasant or well-balanced men and soon met their ends, as did a red-hot poker in the case of one particularly unpopular ruler. Lord Vetinari, on the other hand, is very, very sane. And still alive.
He appears to have survived by being equally distrusted and disliked by all interest groups in the city but also by carefully not being as unpopular as every interest group is to all the others.
A popular form of punishment and mass entertainment in the reign of Mad Lord Snapcase was the tearing to pieces of criminals by teams of wild horses. Lord Vetinari appears to be like the man in the middle of the arena who had managed somehow to chain all the wold horses to one another and is groaning theatrically while watching them drag one another to their knees. The result, in political terms, is stability achieved by equal tension in all directions.
His genius lies in the realization that everyone craves stability even more than they hunger after justice or truth. Even revolutionary anarchists want stability, so that they have breathing space to fight their real enemies, i.e., those higher than themselves in the revolutionary anarchist council, and those heretics whose definition of revolutionary anarchy differs from their real enemies, i.e., those higher than themselves in the revolutionary anarchist council, and those heretics whose definition of revolutionary anarchy differs from their own by about half a sentence in paragraph 97 of the charter.
This policy is dimly perceived by the more intelligent Guild leaders in the city. Yet when an assassination attempt was made (Men at Arms), the Assassins' Guild themselves were prominent in the search for the perpetrator. Annoying as the Patrician is, it is so easy to think of someone worse. Technically, Vetinari seems to have given in to every demand of every Guild for years, so the Guilds are driving themselves mad wondering why he is therefore still in charge.
It has been remarked that if the Patrician were thrown to a pack of wolves he would, after chatting to them for a few minutes, have them tearing one another to shreds. It is certainly the case that when he was thrown into one of his own rat-infested, scorpion-filled dungeons [GG] he organized the rats to eat the scorpions and then to bring him food and reading matter. He'd also, years before, secreted a key to the dungeon behind a secret slab. As he wrote in his unpublished MS entitled The Servant, a sort of handbook for the politically ambitious: 'Never build a dungeon that you cannot get out of.'
He is entirely without vices in any normal sense of the word. If he had any, we can be sure some Guild or other would have made use of them by now.
It is true that he has banned street theatre and hangs mime artists upside down in a scorpion pit opposite a sign that says 'Learn The Words', but this may be considered an excusable peccadillo or possibly an amusing character trait. He does have a small and very old terrier, called Wuffles, to which he is said to be quite attached (although it has not been seen in recent volumes and presumably even despotic rulers have a sad patch of earth behind the toolshed).
Probably his greatest enemy is Captain (later Commander) Vimes of the City Watch but, strangely, the person with whom he gets on best - or least badly - is Corporal (later Captain) Carrot Ironfoundersson of the same Watch. They share the same obsessive interest in the city itself.
Lord Vetinari lives in what was once the royal family's Winter Palace in Morpork (the summer palace is a long way from the city, and the reason will easily be appreciated by anyone who has spent a summer near the river). He manages the city either from a wooden seat at the foot of the steps on which is the ancient golden throne of the city, or more usually from the Oblong Office, high in the palace.
This is where he gathers information. People tell him things, for all sorts of reasons. He has a bedroom. He presumably sleeps.
The Patrician has expressed a wish that, one day, he could retire and cultivate a garden. It will probably never happen. It is impossible to imagine him as a mere civilian. But if he did indeed take up horticulture, the roses would grow in lines, the garden would bloom on command - and the slugs would eat the caterpillars.

Standards, Ankh-Morporkian. [excerpt]
Bureau officials still maintain a small programme of tests of, for instance, the degree of similarity of any two peas or the alcoholic tendencies of newts. It is vital, as the current Patrician has noted, that something like this is found for people with minds like that to do, otherwise they might do anything.

Street Theatre (prohibition of).
Street theatre and mime artistry are banned in Ankh-Morpork under one of the strictest city ordinances (fire eaters and jugglers are considered acceptable, provided they are good at it and can pass the exam; in the case of jugglers, this consists of juggling six razor-sharp knives and a live cat. It is seldom necessary to take the exam a second time).
The unusually inflexible rule has led to the development of street theatre as a criminal activity and those who feel inexorably drawn to looking like a dumb tit in white makeup or hectoring people while doing something dull with a diabolo live a disparate existence outside of the law. Many of them have more mundane jobs as a cover, but they can be spotted by their tendency to unicycle when then think no one is looking.
If caught, they are imprisoned and tortured, usually by being put in a cell with one another (although scorpions also often feature). No one is certain why the Patrician, who has a relaxed approach to assassins and thieves, has this particular quirk, but the citizens of Ankh-Morpork seem quite happy to accept it.

Wuffles.
Lord Vetinari's pet dog. A small, toothless and exceedingly elderly wire-haired terrier with a bristly stub of a tail, who smells bad and wheezes at people. He also has halitosis.