Skill Based System
There are two games out there that I've found are truly "skill-based," meaning no actual attributes. Unfortunately, both are also pretty niche with regards to their settings.
One is Elite: Dangerous, an adaptation of the fourth Elite open-ended spaceflight simulator game (d10 + Skill Mod + mods from enhancements/abilities vs. a TN). The other is The Troubleshooters!, from the Swedish company Helmgast, an althist-60s-era spy-adventure game inspired by that genre of Franco-Belgian comics (d%, roll under skill + mods, with some interesting gameplay mechanics added in). The former system is...sufficient on its merits; the latter fits its genre well, and the mechanics lend themselves to creative gameplay. (I've ditched the less-realistic aspects of the setting for my campaigns. :) )