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Neil Gaiman - More on the Fantasy side than irony. His works are still a pleasure. And ofk his collaboration with Terry "Good Omen". Also check "American Gods" and "Anansi Boys".

Kurt Vonnegut - Not what you would call "Fun and laugh" works, but his stories are crazy, well written and full of irony and smart social critics.

There's always Neil Gaiman. His style is definitely different, but you can feel some similarities. He and Pratchett wrote Good Omens together. Check out Stardust, the Graveyard Book, or American Gods. And of course The Sandman, but it is darker.

Try the stories of Harry Harrison.

Maybe check out Christopher Moore

Definitely read some Wodehouse.

Edit: Stanisław Lem's Pirx series as well!

I think a lot of the comments are focusing on similar subject veins, but for similar writing styles as you asked, I would suggest checking out Christopher Moore or jason pargin( former pen name David Wong)

Phule’s series might tickle your fancy:

https://www.goodreads.com/book/show/505064.Phule_s_Company

I'd definitely agree with the people recommending Robert Rankin.

Tom Sharpe is also funny (Wilt, Porterhouse Blue, etc.)

Also (disclaimer that it's by someone I used to know which may affect my judgement) Go Up by Simon Broadbent is clearly influenced by the Terry Pratchett books set in Ankh Morpork.

I didn't like it quite as much, and it is more middle grade, but A Wizard's Guide to Defensive Baking feels kind of Pratchett influenced.

Give Robert Rankin a Google. The Brentford trilogy is amazing.

I recently read The Stranger Times by Caimh McDonnell, an urban fantasy about a tabloid reporting on supernatural events that's very tongue in cheek and although the humour doesn't always hit, it did remind me of Rivers of London by ways of Terry Pratchett. The characters are certainly very Pratchett-ian. The story starts of with the Stranger Times looking for a "new Tina" a.k.a. assistent editor because the editor is insufferably rude and terrible to people. The job description reads: "Publication seeks desperate human being with capability to form sentences, using the English language. No imbeciles, optimists or Simons need apply."

Tom Holt is much in a similar vein as Pratchett (even shared the same cover artist for a while) with his satirical takes on fantasy & fairy tale tropes.

Surprised no one has mentioned Robert Rankin, who has a darker view that Adams but is good at satirical takes, even though some of his works do feel dated since they were written for the contemporary audience of the publications time.

Diana Wynne Jones is also recommended, she was an influence on Pratchett to a degree. She picks apart a lot of fantasy tropes in her books. she was also a friend and teacher to Gaiman. Most people know her for the Ghibli adaptation of her book Howl's Moving Castle.

Jasper Forrde has been described to me as like Adams but haven't read his book yet.

and finally the Gormenghast series by Mervyn Peake, which was referenced a lot in the early Discworld novels.

There’s also “Rats, Bats and Vats” and its sequel by David Freer and Eric Flint. I like both authors in general as well.

I'm not sure if it will scratch that itch, but Pratchett's daughter Rhiannon is co-releasing something Discworld related in the near future.

I'm mostly in the same boat, except I haven't been able to pick up the Shepherd's Crown. I'm still not ready for it to be over.

Craig Shaw Gardner's Ebenezum/ Wuntvor trilogies are fantasy comedy.

Philip Jose Farmer (as Kilgore Trout) wrote Venus on the Half Shell as a sci fi comedy.

(On the topic of Kilgore Trout - that pseudonym is actually a character from several of Kurt Vonnegut's books - also mentioned in this thread.)

Yahtzee Croshaw (the Zero Punction guy) has also written several fantasy and sci fi comedy books - Jacques McKeown is one series.

Glen Cook, more famous for the Black Company series - also writes a fantasy comedy series - Garrett P.I..

Steven Erikson, more famous for the Malazan books - also writes a sci-fi comedy series - Wilful Child.

The Rivers of London series by Ben Aarronovich; It's a police procedural set in a world where magic is real, and exploited by dangerous criminal groups. The book's protagonist is (initially) a trainee magic-cop in a centuries-old division of the Metropolitan Police.

You should check out Intergalactic Exterminators, Inc by Ash Bishop. I believe it's his only book so far but seems like it's gonna be a series. Its similar to the hitchhikers guide in that it's a bumbling earthling thrown into an intergalactic adventure with all sorts of aliens and weird outer space stuff. Pretty funny too.

Commenting as a bookmark

One that reminded me a lot of Discworld was the Magic 2.0 series by Scott Meyer. First book was called Off to be the Wizard.

Those two are hard to top!

You may enjoy 'Tuf's Voyaging'. An early G.r.r. Martin novel, about some dude space traveling.

It's more pulpy, but if you're fantasy starved, try Jack Vance (especially the Dying Earth series).
He's a very prolific and inventive writer. DnD pretty much copied his magic system.

Jack Handey's short stuff is probably his most famous work, but he also wrote a novel called The Stench of Honolulu.

John Swartzwelder is another comedy legend, he wrote nearly 60 episodes of The Simpsons, and he has a series of detective-pastiche novels (maybe novellas), starting with The Time Machine Did It.

I like these books and think they're along the same lines as Pratchett and Adams, but they are distinctly sillier.

It's actually a very dark book in some points, but Joseph Heller's Catch-22 is that style of absurdist humor set during World War II. My English teacher assigned that one to me when he found out I loved Hitchhiker's Guide.

I second (third? fourth?) the Kurt Vonnegut suggestions too. I have never regretted reading anything with his name on it.

Maybe Ernie Cline, Ready Player One and Armada or Andy Weir, The Martian, Artemis, Project Hail Mary

Maybe Ernie Cline, Ready Player One and Armada or Andy Weir, The Martian, Artemis, Project Hail Mary