There's Quest RPG. It's a simple system that's meant to be an introduction for RPGs in general. They do the degrees of success thing with a d20. I looked into it as a lighter, more story focused alternative to 5e and used the dice roll mechanic to run an improvised game for my kid niece and nephew that went pretty well.

There's also a mech game called Salvage Union that uses the same system. Don't know if there are any others.

There are lots of systems that have varied results. 2d20 and storypath both use a required number of successes to create space for partial success for example.

Freeform Universal uses 6 results (no-and; no; no-but; yes-but; yes; yes-and)

Genesys/Starwars FFG has a dual symbol system which has success/failure tracked separately from advantages/complications. There's also two critical symbols which do not cancel even though one is good and one is bad. You could potentially get a roll which is very good & very bad at the same time.

Those are just the ones I've played. I'm absolutely sure there's more.

Ironsworn/Starforged has strong hits, weak hits, and misses in the action roll. Your action score is compared to two challenge dice. Beating both is a strong hit, beating one is a weak hit, otherwise it's a miss.

The One Ring 2E has a success/fail system that kind of works like that. There are several degrees of success and failure: extraordinary success, great success, ordinary success, failure or success with woe, failure with woe, disaster.

Successes are determined by the die role (d12 and 0-6 d6), and degrees of failure are set (somewhat arbitrarily) by the loremaster.

I've only done a few sessions with my group, but it has proven to be a fun and interesting change from D&D.

So my favorite system right now is CORE. The resolution mechanic breaks down into a combination of Yes/No and And/But. So for instance you can get an okay result that is "Yes, But" where you succeed but at a cost. You could also fail spectacularly with a "No, And" where not only do your not succeed but something even worse happens. The only thing there isn't a result for is just a straight up "No" because that doesn't help move the story along.

Magical Kitties Save the Day! Has Failure/Success, But.../Success/Success, And.../Super Success! — partial successes and failures get "Complications" and extra-successful results trigger a "Bonus"

@simblanco Ironsworn has Strong Hit / Weak Hit / Miss (which are used for everything, not just combat).

Technically PF2e has Crit Success, Success, Failure and Crit failure, but I somehow I don't think you are looking for that if you want something similar to PbtA haha.

Fate has "succeed with style", "succeed", "tie", "succeed with cost".

Success with style usually gets you more than you were aiming for. You scale the wall and also find a fire escape to help your friends up. You stab him real good and also knock him flat. Note that those are typically Aspects you make up on the spot, not stuff you pick from a list.

Usually when you tie you get a lesser version. You try to set the room on fire but only the curtains catch. You try to disable the cameras but only get them to reboot.

Failures mean you don't get it. The cameras stay on. You miss your swing. You can't get up the wall.

But that's kind of boring. You can choose to convert a tie to "success with minor cost" or failure to "success at serious cost". Maybe you set off an alarm. Maybe you get recognized by a rival. Maybe when you swing at the mugger you seriously injure him and he's bleeding out dude what the fuck.

For most rolls you can spend your metacurrency of fate points to bump up your result. "it looks like I can't climb the wall, but I'm Retired Cat Burglar so it comes back to me pretty quick".

But if you spend on everything you'll run out. You should look for compels (things about your character that make the story more Interesting) to get more. "Yo I'm Wanted in 37 states what if the hotel we're breaking into is like a cop convention?" "I'm Fashion Over Form can we say that everyone recognizes me as I try to get away, blowing my cover?". Etc.

Anyway I like this system. I like having more agency. When I played pbta stuff I felt like I was always rolling meh, and the consequences weren't fun. That may have been lackluster GMs though.

The Wildsea has a very interesting implementation of this system. In effect you can have a “twist” with a partial success wherein the other players at the table and suggest what that twist is. https://felixisaacs.itch.io/thewildsea

!pbta@ttrpg.network is what you are looking for. ;)

For a somewhat older overview, this blog post has a nice diagram.

I think I misunderstand your question.

You are aware that both PbtA and forged in the dark are rules systems that each have easily over 100 games associated with them, right?

On drive thru, sorting by PbtA, you get 800+ products.

Do you want game recommendations within these rulesets?

Off the top of my head, here are some I haven't seen mentioned yet:

I've only flipped through the rules, but I believe Call of Cthulhu (and by extension, it's derivatives) has degrees of success/failure.

Mutants and Masterminds has it too.

Systems with a single d6 resolution mechanic tend to have it as well (like Freeform Universal and Neon City Overdrive.)

Some systems, like Black Sword Hack don't really have degrees of success/failure, but a near success can be ruled a "yes, but" at the GM's discretion.