The gaming system created and used by Guardians of Order in their Silver Age Sentenels (using the mechanics with a d10) and Big Eyes, Small Mouth (with a d6) role playing games. The most recent iteration of this system is known as Tri-Stat dX, which allows the game mechanics to be based on any type of die.
Tri-Stat uses three statistics (Body, Mind, Soul), the score of each being in a range from 0 to twice the highest roll on the die used (12 for BESM, 20 for Silver Age Sentenels, etc.) These scores are then used to figure out other values such as those relating to combat, health, and energy/stamina. The system also has a point-based Attribute/Defect subsystem, and many different skills.
The new Tri-Stat dX is available for free from RPGNow as a PDF, or retails for $10 USD, as Guardians of Order claims that their system is more open than the more popular d20 System from Wizards of the Coast. Another reason behind this move is to foster interest in the Magnum Opus imprint run by Guardians. Of course, to actually produce and publish anything using Tri-Stat dX, you have to pay a licensing fee (unlike with the d20 System).