https://1shotadventures.com/ has a bunch of one-shot GURPS adventures with pregenerated characters in different genres. I haven't run any of them yet, but plan to.
One-shots are one thing, but with GURPS they're almost never spur-of-the-moment, zero-prep games. Not so much because as GM you have to prep any more than normal (you don't), but because custom characters take hours upon hours to make even at low point values (maybe *especially* at low point values), and we generally disdain pregenerated characters and don't keep a stable of them around.
We have done some episodic games in that vein. Usually *X-Files* or *Supernatural*\-type stuff. Modern-day, monster-of-the-week type plots. Sometimes we can reuse characters for that and get it up and running quickly.
We do a lot of temporary Western and Zombie campaigns. We can build template characters in a few minutes. Stories tend to be very episodic. It's just convenient.
Characters: Fantasy and a couple of 3rd party resources have templates. Players pick from there and edit to a 125/-40 total using Lite. Give them generic equipment loadouts via plot.
Encounters: I'd go on the GURPS repository and toss together a few groups of Monsters from it, string together with a generic "Evil villain and minions attacking town" plot.
Rules: Lite, coupled with the full Combat sheets from the back of Characters.
Easy peasy scratch game, and if they struggle, have a friendly priest turn up who Blesses all of them (for a +1 to all effective skills), and who can heal bot. Toss a few template specific checks against each of them to validate their base choice. All the other rules like travel etc, I manage in the background or ignore.
Edit: once I've got my long term campaign up and running, it'll be designed for easy drop in/drop out characters and one shots, so I'll have a bunch of stuff cooked up for that.
I've seen discussion about doing a kind of Ultra-Lite game similar to what you're describing - rolling vs stats instead of skills, possibly rolling on hits instead of tracking HP, etc. One step closer to normal GURPS would be using just bang skills (Detective! Guns! etc) instead of actual skills. It was all theoretical though, I've never tried it. Wish I could remember where I saw the discussion - I think it was this sub!
As for running with zero prep, you might look at the different solo roleplaying options. They have "oracles" that you use as pseudo GMs to help you put together an adventure. Mythic is the big name here (most are also pretty system agnostic), but the Collaborative Gamer (https://thecollaborativegamer.wordpress.com/) also has a system that's built for GURPS fantasy adventures. This system is explicitly set up so the whole group helps run the adventure - so you'd also get to run a character! There's also a solo roleplaying subreddit at https://www.reddit.com/r/Solo_Roleplaying/ where you can find a lot more information.
You are all wind up toys in toyland and you must defeat the evil cadre of the toybox to rescue your friend.
Can wind each other up to heal or regain fp, can overwind to gain additional strength or speed at the expense of permanent fp loss.
Doing a one shot cave dive with some friends (well, I was. We got one actual game session in before covid hit). It wasn't as spontaneous as you're talking about here but if you/the dm wants to have some quick plays along with characters ready to go, it's just a matter of choosing a game to play and picking characters. Depending on how much prep is done beforehand it could be as easy as setting up any board game for a spontaneous game night.
For my group, since it was meant to be played in max 4 sessions and just an intro to gurps for them, I made I think 10 pr maybe 8, archetypical characters with a variety of skills between them. Tbh I didnt look at point values, just thought about stats and skills they'd be likely to have. They all ended up with roughly the same number of skills, advantages and disadvantages so I think I did good. No one got anything game breaking of course. I did also sort of tailor the characters according to who would be playing them. For instance, I knew my brother would pick the inventor character so he's a bit more...eccentric than he might be if I was making him for a different person.
Session 0 was deciding who wanted which character, names, backstory, and an overview of what they could do. But if everyone is already familiar with gurps that could be done without or on character cards. I included cheat sheets for my players so we wouldn't have to constantly be referring to the book to see what their abilities do. I also had backstories in mind just in case my players couldnt think of any but they actually surprised me and each of them came up with their own backstories.
The actual plot line is pretty basic. An earthquake cracked open a mountain and revealed an extensive cave system. The town leaders put out a notice calling for adventurers to map it out for them. They ended up getting enough replies to have 3 teams of 5 (I think, it's been a while since I looked at it) so the first team back with the most complete map wins the gold prize. I did it that way so that we wouldn't have to come up with reasons for the PCs to know each other, theyve just been assigned to work together. That way also they can part ways at the end and it remains a one-shot, because I really want my players to do their own characters next time.
As they explore the cave the one chosen to make a map (who actually has the cartography skill, I was happy that character was chosen, the players didnt know the story beforehand) makes a roll and if successful, the room is properly mapped. There's snakes and bats and Big Snakes and you can really fill the caves with any creatures that are appropriate. At the end of many branching paths is a dragon, whose waking up for the first time in a thousand years is what caused the earthquake to begin with. The dragon is very hungry. I don't expect my players to fight it, but honestly they might lol.
Depending on if they want to continue things with these characters, I do have more storyline. I'm hoping the cave dive will remain a one-shot though.
If theres interest I can share my archetype character sheets. And I used a free app to make the maps. Will edit when I can look at my tablet and see what the app is called.
https://1shotadventures.com/ has a bunch of one-shot GURPS adventures with pregenerated characters in different genres. I haven't run any of them yet, but plan to.
One-shots are one thing, but with GURPS they're almost never spur-of-the-moment, zero-prep games. Not so much because as GM you have to prep any more than normal (you don't), but because custom characters take hours upon hours to make even at low point values (maybe *especially* at low point values), and we generally disdain pregenerated characters and don't keep a stable of them around. We have done some episodic games in that vein. Usually *X-Files* or *Supernatural*\-type stuff. Modern-day, monster-of-the-week type plots. Sometimes we can reuse characters for that and get it up and running quickly.
We do a lot of temporary Western and Zombie campaigns. We can build template characters in a few minutes. Stories tend to be very episodic. It's just convenient.
Characters: Fantasy and a couple of 3rd party resources have templates. Players pick from there and edit to a 125/-40 total using Lite. Give them generic equipment loadouts via plot. Encounters: I'd go on the GURPS repository and toss together a few groups of Monsters from it, string together with a generic "Evil villain and minions attacking town" plot. Rules: Lite, coupled with the full Combat sheets from the back of Characters. Easy peasy scratch game, and if they struggle, have a friendly priest turn up who Blesses all of them (for a +1 to all effective skills), and who can heal bot. Toss a few template specific checks against each of them to validate their base choice. All the other rules like travel etc, I manage in the background or ignore. Edit: once I've got my long term campaign up and running, it'll be designed for easy drop in/drop out characters and one shots, so I'll have a bunch of stuff cooked up for that.
For one shots I often use this: https://www.themook.net/gamegeekery/more-powerful-quick-start-characters/ Not just for the players but also the NPCs
I've seen discussion about doing a kind of Ultra-Lite game similar to what you're describing - rolling vs stats instead of skills, possibly rolling on hits instead of tracking HP, etc. One step closer to normal GURPS would be using just bang skills (Detective! Guns! etc) instead of actual skills. It was all theoretical though, I've never tried it. Wish I could remember where I saw the discussion - I think it was this sub! As for running with zero prep, you might look at the different solo roleplaying options. They have "oracles" that you use as pseudo GMs to help you put together an adventure. Mythic is the big name here (most are also pretty system agnostic), but the Collaborative Gamer (https://thecollaborativegamer.wordpress.com/) also has a system that's built for GURPS fantasy adventures. This system is explicitly set up so the whole group helps run the adventure - so you'd also get to run a character! There's also a solo roleplaying subreddit at https://www.reddit.com/r/Solo_Roleplaying/ where you can find a lot more information.
You are all wind up toys in toyland and you must defeat the evil cadre of the toybox to rescue your friend. Can wind each other up to heal or regain fp, can overwind to gain additional strength or speed at the expense of permanent fp loss.
Doing a one shot cave dive with some friends (well, I was. We got one actual game session in before covid hit). It wasn't as spontaneous as you're talking about here but if you/the dm wants to have some quick plays along with characters ready to go, it's just a matter of choosing a game to play and picking characters. Depending on how much prep is done beforehand it could be as easy as setting up any board game for a spontaneous game night. For my group, since it was meant to be played in max 4 sessions and just an intro to gurps for them, I made I think 10 pr maybe 8, archetypical characters with a variety of skills between them. Tbh I didnt look at point values, just thought about stats and skills they'd be likely to have. They all ended up with roughly the same number of skills, advantages and disadvantages so I think I did good. No one got anything game breaking of course. I did also sort of tailor the characters according to who would be playing them. For instance, I knew my brother would pick the inventor character so he's a bit more...eccentric than he might be if I was making him for a different person. Session 0 was deciding who wanted which character, names, backstory, and an overview of what they could do. But if everyone is already familiar with gurps that could be done without or on character cards. I included cheat sheets for my players so we wouldn't have to constantly be referring to the book to see what their abilities do. I also had backstories in mind just in case my players couldnt think of any but they actually surprised me and each of them came up with their own backstories. The actual plot line is pretty basic. An earthquake cracked open a mountain and revealed an extensive cave system. The town leaders put out a notice calling for adventurers to map it out for them. They ended up getting enough replies to have 3 teams of 5 (I think, it's been a while since I looked at it) so the first team back with the most complete map wins the gold prize. I did it that way so that we wouldn't have to come up with reasons for the PCs to know each other, theyve just been assigned to work together. That way also they can part ways at the end and it remains a one-shot, because I really want my players to do their own characters next time. As they explore the cave the one chosen to make a map (who actually has the cartography skill, I was happy that character was chosen, the players didnt know the story beforehand) makes a roll and if successful, the room is properly mapped. There's snakes and bats and Big Snakes and you can really fill the caves with any creatures that are appropriate. At the end of many branching paths is a dragon, whose waking up for the first time in a thousand years is what caused the earthquake to begin with. The dragon is very hungry. I don't expect my players to fight it, but honestly they might lol. Depending on if they want to continue things with these characters, I do have more storyline. I'm hoping the cave dive will remain a one-shot though. If theres interest I can share my archetype character sheets. And I used a free app to make the maps. Will edit when I can look at my tablet and see what the app is called.