Death and the Luggage. I thought it was so cute when the Luggage got a girlfriend!
Agnes Nitt and Detritus. Not as a couple, mind you; that would be silly…
Perdita X and Detritus, on the other hand… 
I also rather like Gaspode, especially after he hooks up with the beggars.
And the Faculty as a whole. Their sojourn on the beach in The Last Continent was beautiful.
I like all of em, but DEATH is somebody I just go ahead and laugh about whenever he’s mentioned just to get it out of the way.
I also like Nanny Ogg, because Pratchett makes her out to be much more powerful and influential than she lets on. For isntance, she’s got pictures of all her children, grandchildren and great grandchildren in her parlor, but arranged by pecking order. If one of her descendents fell out of favor with her, she’d move their picture down to the bottom rung.
He also described how she ran a master spy ring, mainly because she had that act of being friendly down to an occult science. She remembered every single conversation she ever had and used that storehouse of knowledge to conduct her plots and scheming. She got that info by just being nice to people. She’d just go up to somebody, engage in pleasant conversation, ask how their mother was doing, then work in a key question by making it sound completely innocuous, and finish off the conversation with more droll pleasantries. Classic!
Just to be different, I’ll vote for the dwarf who wears dresses (forgot her name).
Nanny Ogg is the sort of boozy old lady I hope to be someday. Though hopefully I won’t terrorize my family quite as much as she does hers.
Cheery Littlebottom is the dwarf who wears dresses. I really like her, too, FriendRob.
Well it depends on the circumstances:
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I want to grow up to be like Captain Carrot
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I am unfortunately attracted to food served by the likes of C.M.O.T. Dibbler (sausage inna bun!)
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Commander Vimes is my kind of policeman, and Lord Vetinari is my kind of politician (‘Do not let me detain you!’). Vetinari is not necessarily nice, but he is ruthlessly efficient.
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I fully understand Sergeant Colon (who wants to do outdoor duty on a windswept rainy night?)
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if only I had the brains of Leonard of Quirm (sigh)
I suppose on tie-break Carrot loses out to William De Worde, who overcomes his upbringing to be a truthful man.
P.S. I looked for the dwarf in the skirt in ‘The Truth’ (starring William as above), and she wasn’t named in the paragraph I found!
I’m sure she’s a corporal…
I think Nijel the Destroyer was the son of Harebut the Greengrocer. What a name!
One of my favorite scenes also comes from Moving Pictures. I can’t remember it exactly but it was when the Librarian was getting ready to go into Tarzan mode. He beat his chest and cried out. Then he coughed and decided to wait until all the purple lights had gone away.
That and when he attacked the University organ after hearing the Band with Rocks In. Great scene, great scene.
In no particular order:
DEATH - Simply hilarious. I love his attempts to lighten things up, which never seem to work out. He also has the best “last word” lines (of course!).
The Librarian - Another great character. A gentle scholar who can twist your head off. Like photpat, I love the scenes with him (the Librarian, not photopat) blasting away on the organ.
Vimes - especially when he’s being rude to some muckity-muck, as well as the reactions he gets out of Nobby and Colon - “He’ll go spare! He’ll go completely Librarian-poo!”
The Luggage - I think the Luggage is what we all want to be when we get up cranky. It’s not evil, just very, very angry.
And one I haven’t seem mentioned - “Bloody Stupid” Johnson. Although we never actually see him, Pratchett’s descriptions of his work are enough to get me giggling out loud. Like the fish pond that is 20’ long, and six inches wide (don’t know if those are the exact measurements, but you get the idea).