I've mentioned this before: I have an uncle who started most of my early reading obsessions by giving books for birthdays and Christmas.  When I was 14, my uncle gave me my first Discworld books, Men at Arms and Soul Music.  I was thrown right into the middle of the series without any background, and I loved them.  I've since acquired nearly all his other books from the Discworld series and otherwise, and a number of other tie-in media, like almanacs, maps, TV adaptations, video games, and even a cookbook.

It is Britsh comic fantasy, a bit like a more refined Hitchhiker's Guide to the Galaxy.  Terry Pratchett recognizes the tropes of fantasy and mythology but plays with them to build his stories.  Characters in the novels know this, and their actions are often guided by that knowledge (the hero wins, the no-name thug will die, 1-in-a-million chances come up 9 times out of 10, the mysterious stranger is obviously up to something, etc.)

For people who want literature for their kids, this series is good for it:  Terry Pratchett weaves a lot of social commentary into the stories.  Using fantasy standards such as trolls, elves, dwarves, werewolves, vampires and such as stand-ins for various cultures, he addresses a lot of modern issues such as racism and intolerance, gangs and violence, and even large-scale economics and terrorism, all without coming across as preachy.

I wouldn't recommend starting at the beginning; Terry Pratchett didn't really hit his stride until about 10 books (of 39 so far), at around Reaper Man.  This is where a lot of the fantasy elements and straight-up jokes are played down and the character and character-driven humour take over.  Even then, there are quite of number of cross-genre mashups here, including detective, noire, military, comedy, martial arts, murder mystery, pop culture, kids books, etc.

The series itself can be divided into several sub-series, in addition to a number of standalone works, though all of them do have appearances by characters from each subgroup:

The City Watch (my personal favourite)
The Witches
Rincewind and the Wizards
Death (he's actually a nice guy, and pretty thoughtful, too, even if he doesn't understand people very well)

Plots don't span multiple novels, but there is a lot of progression in characters and the world in general as people are promoted and technology marches on so reading them in rough order is recommended but not required.