Tabletop, DnD, board games, and minecraft. Also Animal Crossing.
3rd International Volunteer Brigade (Hexbear gaming discord)
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Bloobs adventure idle is an incremental game that's basically what if runescape but inventory stacking and autopathing. It's more active than most incrementals but maybe still more idle than you like?
Dwarf fortress maybe? particularly if you slow game speed a bit. you can designate stuff, set up management orders, and mostly wait for it to get done. It's possible to be in very safe places and the game will usually pause if something significant happens (can disable for even more self running).
I'd like to find a game that's similar to this but the game doesn't have to be open. Like a single player game that I can play for a while but then stuff continues to happen while I am at work, like EVE's player leveling system or other MMOs with similar mechanics. The only mechanics I've found like that in single player games are dumb crafting things that happen in real time.
The Gnorp Apologue is a great idler game. 96% positive on steam.
Cookie Clicker is an oldie but it's a classic.
Loop Hero?
IdleRPG (typically hosted on various IRC networks) is kind of a canonical example of taking this idea to the extreme.
Rusty's Retirement
Red Rogue has a mode where it it pauses when you're not actively moving which makes it super-easy to jump in and out of it.
Check out Orb of Creation, this game is technically an idle game, but you can definitely just keep clicking buttons for hours, but also just stop at any moment.
people have suggested "games like RuneScape" but why not RuneScape itself? it's the OG second monitor game. old school RuneScape isn't really truly afk but the grinds really don't need much attention. if you want a more afk experience then play the regular RuneScape that one has higher xp rates and more actual afk training methods.
If you have powerful enough hardware,
“Full-fat” games designed for a PC experience:
I play Dwarf Fortress like this, you can spend unlimited paused queuing up stuff to do and then whenever you're ready you can just unpause and let the work happen. Its nice too because if something important happens while the dwarves are working the game will auto pause.
Maybe Pixel Starships? You can actively do missions or PvP, but resources accrue automatically. Crew training, building modules and ships is time gated so you can just wait it out. The PvP piece is interesting too, you can only be attacked when you're offline so you have to use the built-in scripting to manage your ship unattended.