Ideas. Amongst the assortment of pastime-related web content that I publish are some original (albeit not necessarily earth-shattering) ideas.
I like to demonstrate them rather than just describe them - so I get to be the first to do them - but once that’s done, they are free for all.
I design games for a living. I also design games for fun in my spare time. If I didn’t have to work, I’d still make games and give them away for free.
I’d also still write. I’ve got a scholarly book on play coming out next year, and I’m working on a second one now. It’s unlikely that either will produce much in the way of royalties, but I think that people will find them useful.
I have also done some writing and game design for free. (Heck, I actually spent more money than I received for it.)
My main job is as an accountant. I would be willing to do about two hours a day of that for free, for the right people. So you might get some productivity out of me in some idealized society, but nowhere near what you get when you pay me.
I also love cooking. My wife and I once catered a wedding for 50 people (no, wait, 75. No, 100. Wait, maybe it’ll be 200. Grrr… but indecisive brides with ballooning guest lists is another issue.) We only asked for the food cost to be paid. But, again… about two hours a day is about my limit for enjoying cooking. I can’t imagine working in the food industry full time.
I suspect that many people feel the same way about their various talents. Maybe you could build an economy out of part-time amateurs, but I don’t think it would be very functional. Frankly, it sounds to me about as rational as Pol Pot insisting we should all go back to preindustrial farming.
I am just like njtt. Before I retired, I taught, went to committee meetings, and did and published research mathematics. Now I just do the latter and occasionally lecture on it. One of my collaborators, just retired, met someone a few days ago who just could not believe he did it for no pay. Getting it published is its own reward. If I didn’t get it published, I would probably slowly quit.
I run a Facebook group for buying and selling used stuff in my area. Mostly kids’ stuff, but some household goods, adult clothes and toys, etc.
I feel like it’s a pretty great service for the community. Stuff gets recycled and people get stuff they need for cheap, and people get some cash for stuff they may have otherwise thrown away or donated (and don’t worry there are still PLENTY of donations). Yes it’s just like Craigslist but it’s “invite only” so it’s way more secure, the moderation is very tight (if you’re a bad buyer or seller, or a bad person, you’re out). We get a lot of stuff done.
I design for the Web for a living and I used to do Web stuff in my spare time, for free and cheap. And computer repair. And they are just thankless, demanding jobs. I can’t bear to do them un-paid anymore, or even outside of my professional capacity. Everyone wants too much from you.
Being a moderator/admin of a group is hard and thankless too, but so far I get enough out of the group itself to keep at it. And it’s funny because even though my FB group has nothing in common with the SDMB I always see the exact same stuff happening with our mods vs members as I see here. People are out. of. their. minds 
Well, like LibrarySpy, I’ve written some fanfic. If I could, I’d research and write more—and producing Dōjinshi looks like it’d be a hoot, if that was really a thing over in the US, meager profit or not.
To say nothing of my original fiction—mostly in the planning stages for now, but something I have some hopes for. But if money were no object, I’d gleefully keep at it.
The same thing with my flight simulator works, although I’ve sadly had to slack off a bit as of late. Aircraft, scenery, weapons, etc. Especially the weapons—I’ve built what has to be in the low hundreds of simulated aircraft weapons, going to trouble and some expense, honing my skills, for a simulator that doesn’t even fully implement combat features, and has a relatively small number of users who do use, or even want them.
I do it for fun, sure, and because it’s a subject that interests me…but, for a not too tiny degree, it’s out of spite. Cold, undying grudges. You can’t put a price tag on that.
And, as a matter of fact, if I won the lottery or had all my needs taken care of, I actually would stay at my job, at least a couple of nights a week. I’m good at it, it’s a nice workout, the environment and hours are nice, I don’t have to talk to customers, and I actually find it a bit relaxing, especially in some of the roles which seem to fray other peoples’ nerves. Hey, “from each according to their ability,” I guess, right?
Word.
I have done this at the kids’ school for years (it’s a small Christian school with no $$$).
If I spend three Sundays a month, all day long, setting up a firewall, installing network switches and NAS devices, configuring auto-installers using wpkg (poor man’s Windows Server), installing virus software, replacing failed hard drives, fixing stuff the kids messed up, I hear nothing…
…until the day I get a phone call “The Internet is down.”
That’s all I ever hear. And the description of the problem is always the same.
In contrast, if I take photos of the kids for their parents, everyone is happy.
Computer work is tedious and truly thankless.
The concept of the book mentioned by the OP is one that I’m fascinated with. It’s one that I’d really like to believe is possible, but it’s not one that I think we, as a species, are ready for, and we probably need greater advancement in technology and infrastructure in order to nearly eliminate all the sorts of jobs that people are unlikely to do for free. That said, since it is a concept I’m fascinated with, I’ve given a fair amount of thought to the idea of what I would do if I were in such a society.
Like several others up thread, I work as a programmer and doing other IT work. In general, most of what I do for my day job is not something I’d be willing to do without some compensation, but it wouldn’t be completely that way. There are certainly some projects I’ve worked on that were interesting enough that I’d be willing to work on them without compensation on my spare time. For example, I enjoy mathematical programming and modeling, I love signal processing and computer vision; several times in undergrad and grad school I went way beyond the requirements for the assignments when I was working on those types of projects and I jump at opportunities to use them in my more mundane projects at work.
That all said, I feel like my greatest contributions aren’t even in my technical skills and they’re things that I already do without any expectation of compensation. Hell, if I could do them in such an economy, I would be able to do them with greater quality and quantity. I’m a musician, and like most artist and crafter types, I’d love to be able to create, record, and share a whole lot more of it. In fact, I expect most artistic or craft types would be like me as well. I also really enjoy a large number of intellectual pursuits, like amateur philosophy, mathematics, science, etc. and I’d be willing to contribute to several of those on my own as well. I enjoy exercise and training, so I regularly help other people out with their routines and such, and I’d continue to do that. And I do actually enjoy some volunteer work, the only reason I do so little of it today is because I end up so busy with these other pursuits, and maybe if I didn’t have to spend so much time doing the work I do to make a living, I’d be able to spend more time with humanitarianism as well.
I think he meant the book in the OP, by Jeremy Rivkin.