I would really love to inflict the Discworld series on everyone I know, but it gets difficult to explain everything about them all to a new reader. So I've banged out this reference to help people make an informed choice about what to read first.
To best select which you should start with, you need to answer a couple questions. His Discworld ones, the most famous and prolific, have several running story lines, all with different themes and feelings. The main ones, and best to start with are: The witches of Lancre, The City Watch, Rincewind, Death and his relatives, or the Industrial Revolution.
The witches’ series is mainly philosophical, with an emphasis on the absurdity of our society and beliefs, and helping to understand our own history of paganism and such. Also focuses quite heavily on morality, (Arguably my favorite brain read). If you read any in order, it is these ones I would recommend to do so; ESPECIALLY the trilogy of Wyrd sisters, Witches abroad, and Lords and Ladies.
The City watch is my current favorite, mostly due to my interest in the military and police work. Focuses on the development of Ankh-Morpork (the main Discworld city), and explores the nature of existentialism, the self, and also Justice. Also includes the bonus character of Vetinari the ruler of Ankh-Morpork, who is arguably the most fascinating character on the Disc. He really steals the show. But then he makes is better, more organized, and sort of gives it back, while still maintaining complete control, and tells you it’s all yours again, but you have to run it exactly how he says because If you don’t, well, nothing bad would happen, but think of your delightful children, and wonderful wife, currently residing at (insert address here)? Wouldn’t they be disappointed in you? Plus he calls himself a tyrant. Rincewind is the best series to start with if you want to understand the climate of the whole Disc. Also discusses the nature of the magic on the Disc and the relationship between our science and the Disc. Includes a focus on the idiosyncrasies of our love for heroes.
Last, but not least, the Death series (ha ha). An all encompassing view of the Discworld (Death himself is present in every novel), with an interest to examining the nature of death, life, the human condition, as well as fate and destiny. Another good series to read in order, as the evolution of the primary two characters, Death and his granddaughter Susan, is quite fascinating. Death actually grows, learns, and changes markedly throughout.
Finally, the Industrial Revolution is a series of books examining the nature of Cities, economics, and, well, revolutions. Also focuses on the development of ankh-Morpork, with a view to the minuet everyday life of the average denizen.
If you wish to start with the Witches, they are the longest running series, starting with Equal Rites, moving into Wyrd sisters, Witches abroad, Lords and Ladies, Carpe Jugulum, then Masquerade, also involving the City watch somewhat, then Wee free men, Hat Full of sky, and Wintersmith. This series includes two short stories I have been unable to locate called “The Little Fish and the sea” and some other one possibly involving pink.
To start the City Watch series, you should begin with Men at Arms, Guards! Guards!, Feet of Clay, Jingo (my longest running favorite), The Fifth Elephant, Nightwatch, then Thud!. If you would like to mesh them, Masquerade would be read in between Jingo and The Fifth Elephant.
The Rincewind novels start with the first Discworld novel, but have not been updated in a while. They begin Color of Magic, The Light Fantastic, Sorcery, Faust (Eric), Interesting Times, The Last Continent, and finally The Last Hero. This series, if read with the Witches, should be read in an alternating fashion. For the witches and wizards meet in Lords and Ladies and there is some confusion over headmasters at Unseen University (the main place for the Rincewind series). Equal Rites should be read after Color of Magic but before Sorcery, as the head Witch takes a trip to the University and meets the headmaster. The Last Hero should be read in between The Fifth Elephant and Nightwatch as it involves a main City Watch character.
The Industrial Revolution series is short, Moving Pictures, The Truth, Monstrous Regiment, Going Postal, then the newest addition, Making Money. This should not be started until after Jingo, Interesting Times, and Masquerade, since it will affect your perception of Ankh-Morpork.
The Death Series, although he is in every book, is primarily: Mort, Reaper man, Soul Music also involving the wizards, Hogfather, then Thief of Time. Soul Music should be read before Interesting Times, and Hogfather should be read after Jingo.
There are a few random books which sort of have an order; Pyramids and Small Gods should be read before Thief of Time, and Carpe Jugulum. The Science books (The science of Discworld I, II, III) can be read any time after The Last Continent. The Amazing Maurice and his Educated Rodents should be read by candlelight in the tub, to achieve the full effect, but other than that, go nuts.