Savage Worlds - Pulpy Action-oriented system, tons of setting books, has e.g. an official Pathfinder rulebook. Uses exploding dice balanced out by "bennies" and "wild dice". Lots of fun IMO, I especially liked when my Shadowrun 2e game converted to the Sprawlrunners Savage Worlds rules, combat and hacking went much faster and was a lot more fun to play. My current multiverse based dimension-hopping campaign is using this system and it's been a barrel of fun. I feel no need to fudge dice since the players can choose to spend a bennie to re-roll when it matters to them. Running out of bennies is basically like the character running out of luck, so it's very cinematic in that way.

Freeform Universal - totally free system (as in it's Creative Commons). No GM dice rolls. Players roll dice only when both success and failure are interesting. Has some similarities with Savage Worlds in terms of player agency and a system similar to bennies.

Basic Roleplaying - Percentile-based d100 system. Used for RuneQuest and Call of Cthulhu. Perhaps the best system for a simulationist approach due to all skills being a number from 0-100 that shows the exact percentage of the time the character will succeed. This means there's very little mathematical crunch and the extremely straightforward stats always tell you at a glance what your odds are going to be in any roll. I haven't personally played it but I find this design incredibly elegant.