Favorite: (and I realize I’m all alone in this opinion) is Moving Pictures.
Runners Up: Witches Abroad, Hogfather and Men at Arms.
And I can’t wait for The Last Hero (coming soon to a bookstore near YOU!)
Fenris
In no particular order: Hogfather, Feet of Clay, Mort, Reaperman, Wyrd Sisters, Lords and Ladies - are the ones that come to mind first.
I don’t quite agree that he is improving all the time - he started up at the top and more or less stayed there, and his books are stil very good, and I still buy them as soon as they’re out in paperback, butI think he’s in a bit of a formula rut now. The first eight-ten were much more original than the last few.
I would say that the best way to read them is in chronological order of writing, because he does change the characters as he goes on, and it’s interesting to see the developments in, for example, Death, or the way the trolls speak. But I don’t suppose it matters.
Let me disagree with myself before someone else does - NOT “much more original”, just “somewhat more original”. At the end of the day, even a bad Pratchett is as good as or better than many other people’s best
Favorite book? Wyrd Sisters, Mort and The Truth come to mind.
Favorite character? Granny Weatherwax, Rincewind and DEATH (also Death of Rats). I think I identify with Granny in a lot of ways…scary…
The first one I read was “Small Gods”, which I still think is one of the best, although it and “Pyramids” are sort of one-off’s. At that point, I decided I should read them in order. BTW, “Pyramids” is one of the lesser ones, IMO.
I like the witches - “Wyrd Sisters” was one of my favorites. I don’t like the ones with Death as much as other people seem to - I didn’t like “Mort” as much as some others, for instance. I also like the bits involving the Unseen University - the faculty is a riot, and I’m always amused by their interplay. Samuel Vimes and the Watch are probably Pratchett’s best character development, and I like story lines involving them as well.
I’m always eagerly anticipating the appearance of the Librarian, too. Oook!
My favorite Discworld books would have to include Hogfather, Moving Pictures, Small Gods, Carpe Jugulum, The Fifth Elephant, and The Thief of Time.
I have a fondness for the Patrician, Havelock Vetenari, because of his total mastery of any situation and his dry, understated wit.
I totally forgot about Moving Pictures, Fenris, you are not alone <g>
And how could I forget Gaspode the wonderdog 
Another great character.
Rick
I’ve always had a soft spot for Men at Arms- I wouldn’t call it his best work, but I have this incredible soft spot for the Angua/Carrot scene during the wedding.
I’m reading Thief of Time right now!
Favorites are probably Reaper Man and Hogfather. Rincewind does not interest me at all (though I am quite fond of the Luggage). I do enjoy all the other wizards (Ridcully and the Dean) but Rincewind just doesn’t do a thing for me. Witch books, Watch books, Small Gods, all good.
That’s cool. I left Reaper Man off mine! 
Gaurds! Gaurds! or Soul Music - I can’t decide.
I have to pick one?!?
Forget it, can’t be done. I’ll just read 'em all all over again, and savor each lovely…
(Just finished The Truth last week, and it was a good 'um. Especially loved the Patrician’s discussion of c-commerce…)
I’d probably pick Small Gods, too. Not only is it hilarious, but it also has a surprising amount of depth.
However, I’d also put Mort, Pyramids, Guards! Guards!, and the Granny Weatherwax Shakespeare parodies (i.e., Wyrd Sisters, Witches Abroad, and Lords and Ladies.
Least impressive were Moving Pictures (despite the promise of its premise) and Reaper Man (I love Death, but in smaller doses.)
Also, read Good Omens, written by Pratchett and Neil Gaiman.