Yes! They’re my favorite books, and the only ones I would consider attempting to get the entire series of. I read them from when I was about 10, to maybe a year ago. (I didn’t stop reading them, I just knew them all)
One of my uncles, who I will refer to as Uncle, loves books, and so do I. He gave me either Sourcery (about the 8th son of an 8th son) or The Color of Magic (first book with Twoflower in it, where they see an ocean troll), and I loved it. I’m pretty sure that it was The Color of Magic, but it was quite a while ago, so I may not be remembering it correctly.
I guess that my reading Terry Pratchett made me pick up a few British mannerisms, as I never knew exactly what “Posh” meant, but I used it to describe “fancy”. (Apparently posh means pretending to be fancy/getting ideas above your station) I picked up enough of them that people often thought I was British, but I’m not (I don’t like Marmite that much). When I read The Last Continent, I started saying “G’day mate!” and “No worries!”, so it’s definitely had an influence on me...
I’d say that my favorite books when I was younger were the ones with Rincewind in them. I can kind of identify with a man who just wants to be left to eat his potatoes in peace, but is instead being used as a pawn by forces beyond his control. Now that I’m older, I prefer the Moist Von Lipwig and City Watch books. Why? Because satirical depictions of the police (“Don’t walk too fast towards someone yelling for help, or else you might get there in time”) and of con artists are much funnier and easy to read about than the real thing.
Of the non-Discworld stories, I would say that my favorite single book/short story is The Carpet People, and my favorite series would have to be either the Bromeliad Trilogy or the Long Earth series.
Terry Pratchett’s books are the kind that you can read for fun when you’re a young kid, and then read for fun again when you’re older, but you can recognize some of the slightly less obvious satire.
The companion books are definitely worth reading/having (I have a map of Ankh-Morpork on my wall), but I would say to read almost every other book first.