Because people seem curious....

How Sam Read the Discworld Books.

I'm not including the YA Witches Novels because I haven't read them. I've heard they're excellent. Also excellent are the YA "Bromeliad" trilogy, featuring Nomes who live in a department store until they make a gallant bid for freedom. They're not Discworld, but well worth reading and appropriate for eight-to-twelve year olds.

Right.

There are several "series" of Discworld books, as well as standalones. I recommend trying a standalone or two before you decide whether or not you want to try the serieses. Characters all cross over each other, too, but basically you can pick up any Pratchett book and enjoy it. You'll just enjoy it a lot more if you've read others -- Night Watch, for example, is MUCH more interesting if you've read Feet of Clay, because you'll know Vetinari better and it'll be more interesting to see him as a teenager.

Small Gods -- Standalone
Pratchett's take on comparative religion. The predominating religion in the book, Omnianism, also reappears in the Watch books as a running joke. Small Gods, by the by, is set about a hundred years before any other book -- the rest all take place over the course of about a forty-year span or so. More like a ten-year span if you don't count the time travel in Night Watch.

Pyramids -- Standalone
I come back to this one over and over again because I love the sections about the Assassin's Guild. Pratchett tackles Egyptian mythology/theology. The Assassin's Guild is good to know; it crops up in a lot of the books. This is also the book in which we meet, for the first and last time, Prince Pteppic, who is a much-beloved character (and where Pratchett takes his "Pterry" nickname).

If you like these two you'll probably like most of what Pratchett writes. The serieses are:

The "Watch" series
The Watch series is my personal favourite. Some of Pratchett's most complex heroes and heroines -- Vimes, Sybil, Vetinari, Carrot, and Angua -- grew out of these books. They focus on a small cadre of Watchmen in Ankh Morpork, the biggest urban centre on the disc, as they slowly rise from obscurity to....lesser obscurity. Their hero, Vimes, is a hard-boiled, cynical, mean-as-nails police captain and he's just an utter joy to read. Vetinari also shows up most often in these books, though he appears frequently in the Wizard books as well.

Guards!Guards!
In which Vimes and his sad Night Watch take on a DRAGON.
Men At Arms
Pratchett's take on the firearms debate. Also marriage, gender equality, and werewolves.
Feet of Clay
Vimes chases an unnatural murderer while Vetinari, the Patrician (read: ruler of the city) is slowly being poisoned. Pratchett addresses racism and bigotry in an unusual fashion.
Jingo
Ankh-Morpork prepares for war, and Vimes attempts to prevent it. Deals with war and motivations for war, and also has my all-time favourite literary allusion to Ozymandias in it.
The Fifth Elephant
I can't describe my love for this book. Vimes goes to Uberwald (basically Transylvania in every bad vampire film ever) and gets embroiled in local politics. We also meet Lord Vetinari's former paramour and Angua's family.
The Truth
Nominally a Watch book but really a standalone, The Truth is Pratchett's take on journalism. It introduces some favourite characters, including Otto the Black Ribboner and William de Worde.
The Night Watch
Generally believed to be Pratchett's finest work. Vimes is flung backwards in time, and finds himself mentoring his own younger self in the dark days before the rise of Vetinari. Both Vimes and Vetinari make appearances as adolescents, and Les Mis is satirised, among other things. One of Pratchett's darkest and most complex novels.
Monstrous Regiment
Again, possibly a standalone, though Vimes and William de Worde both make appearances. Not Pratchett's best work, IMO. I didn't finish it.

The "Death and Susan" series:
Death, the character, appears in almost every single book. He's the personification of death; he has the robe and scythe and all the rest. He's also very much linked to archetypal mythology -- many of the books discuss the origins of modern day rituals such as Christmas. His granddaughter Susan is an exceptionally good female character, like Angua in the Watch books.

Mort
In which Death takes an apprentice who, predictably, bollockses things RIGHT up.
Reaper Man
To be honest, this may come before Mort; there's no Mort mention in it. I can't remember what it's about, actually.
Soul Music
This is the one where the Death series really starts to take off. Susan, Death's granddaughter by adoption, meets a young Musician named Bud-y-Holly. Pratchett tackles the rise of rock-and-roll, Discworld style.
The Hogfather
Pratchett addresses the historical traditions of Christmas. Using DEATH. This is both a hilarious book and also rich with mythological symbolism.
The Thief of Time
A maniac invents a clock that might destroy the universe. Susan and an unusual companion must destroy it. Sort of a kung-fu movie meets mythology. Apparently it has a lot of Reservoir Dogs references.

The "Witches" series
The Witches series is predominantly about the power of ancient myth and fable, especially in the rural hill cultures of Great Britain, particularly Scotland. It follows two elder witches (Granny and Nanny) and two younger witches (Magrat and Agnes), though their husbands and sons occasionally make brief appearances.

Equal Rites
Both a Witches and Wizards book, but it's predominantly the Witches. You can read the rest of the series without reading this one; it's not very memorable.
Wyrd Sisters
Something akin to Macbeth, and one of Pratchett's best books about hillcountry mythology and also theatre.
Witches Abroad
Magrat, the dubious heroine of Wyrd Sisters, becomes a Fairy Godmother. Pratchett tackles Faerie Tales.
Lords and Ladies
The witches battle the Fey. Who aren't as nice as one would think, really. People who do morris dance will get an especially big kick out of this one.
Maskerade
The Witches go to Ankh-Morpork (setting of the Watch books). Pratchett satirises Phantom of the Opera. A couple of the Watch show up in cameo spots. An excellent book for Phantom fans.
Carpe Jugulum
The Witches battle vampires. A really interesting take on vampirism. This also gives the origin of the "Black Ribbon" which shows up again in the later Watch books, particularly The Truth.

The "Wizards" series
The Colour of Magic and The Light Fantastic
Two halves of one book. Heavy on the satire of fantasy and scifi novels. Not his best work, but then they were his first two books.
Sourcery
Wizards at war. Still very fantasy-satire oriented.
Eric
Pratchett does Faust. Pretty funny. Faust is replaced with a ten year old. A short and easy read.
Moving Pictures
Could also be considered a standalone. Pratchett satirises the rise of the movie industry and the golden age of film.
Interesting Times
Rincewind, the nominal hero of the Wizard books, travels to the Discworld analogue of China, and helps a peasant revolution.
The Last Continent
Rincewind moves on to Australia, or its equivalent, and uh....does...stuff. It's a really funny take on Aussie culture, but I can't recall the plot in the slightest.

The "Standalones"
The standalones (other than Pyramids and Small Gods) are:

The Truth (Nominally. Could be considered a Watch book)
Monstrous Regiment (see above)
Moving Pictures (Could be considered a Wizards book)

Going Postal
Pratchett's latest novel, tackling the tradition of the Post Office. A little slow moving at first, but picks up quickly and really gallops along towards the end. Vetinari puts in a few memorable appearances. Set in Ankh Morpork, setting of the Watch books.

Commentary post-hack: Thanks to danceswchopstck, light_of_summer, and salammoniac for helping me recover this!