Wikipedia points out that some form of fan fiction has existed for almost as long as publishing, but the modern form and its surge in popularity follows the growth of fantasy writing in general and the career of Terry Pratchett in particular fairly closely. The modern form, wherein amateur writers create new stories around established characters in "universes" created by established writers, may have originated in "fanzines" dedicated to the Star Trek series in the late 1960's.
The Discworld is a very popular setting for fan fiction although it lags far behind a well-known school for wizards, several settings probably unknown to childless adults, and even the world of Pride and Prejudice in submissions to FanFiction.net, the major internet publisher. Good Omens follows fairly closely, moving Pratchettia higher in popularity.
Like every other school of writing, fan fiction is subject to Sturgeon's Revelation, so it is dominated by low-grade and frequently juvenile work, but talented amateurs emerge as elsewhere and occasional gems may be found. Tvtropes points out that the lack of publishers and editors allows all of the worst examples equal exposure on the internet.
Sources of Prachettian FanFic
- FanFiction.net The largest collection of fanfic of all genres
- Our own small selection on the L-Space Web
- Discworld Fanon Wiki - An embryonic but slowly growing guide to the Pratchett fanon