First up is Caltrop Core.  It doesn't get much more basic than this.  I don't remember exactly when I first encountered this system, but it's probably been a year or two.  For those that can't be bothered to click and see for yourself, this system uses d4's to resolve questions that come up in a game.  I have developed a marked dislike for the venerable d20 over the years, so giving some love to the oft-forgotten d4, even if it was just out of spite, appealed to me.  You read each die as follows:

1 Absolute Failure.  You don't get what you want and things get a lot worse.
2 Partial Failure.  You don't get what you want.
3 Partial Success.  You get what you want, but things get complicated.
4 Absolute Success.  You get what you want - and more.

 

As presented, you can either make your Caltrop Core game stat-based or token-based, but either way, as a player, you want to be able to roll as many dice as possible and then use the best result.  I liked this idea, but ultimately, the probability spread didn't work for me. I built a different matrix using d6's that looked like this:

1 Critical Failure, and each 1 beyond the first amplifies the severity.
2-4 Failure.
5 Success, but there may be a complication.
6 Complete Success, and each 6 beyond the first amplifies the benefits.

 

I wound up writing out a dozen pages of rules to support this idea, and I think what I have constitutes a fully formed system, but the way I determined how many dice to roll for each test was a little complicated in non-typical but still common enough circumstances.  About the time I finished it, I found FU by Nathan Russell, which does very much the same thing in a way that is probably better.  *sad trumpet sound*

But then I got distracted...