RPGMemes

GURPS is my go-to system. It's incredibly flexible, both in what it allows you to do as a player, and what kind of game you can run as a GM.

It's an older system, and by default is rather simulationist - it grew out of the same tabletop wargaming that D&D did, and tends to take a more realistic approach to what players can do than more narrative systems. I like some of the more narrative systems as well - Starforged is my other go-to system - but the characters always feel a little more loosely defined to me. GURPS is perfectly happy saying "okay, you can fly, you can turn invisible, and you can't be killed" - but if you want to make your character more nuanced, it's not only possible, but encouraged!

On the other hand, if you just want to throw something together and go, you can do that too! One of my players has a character sheet that consists of their racial abilities, 5 or 6 regular skills, and a high level "Security!" wildcard skill. And 3 guns. They're a nightmare in combat, because "Security!" is their all-in-one skill with pistols and melee combat, along with anything else a person with a security background would be expected to know - it's been rolled against to evaluate patrol schedules, reading a foe's body language, and shadowing a mark, among other things. That character plays alongside someone with three different templates (classes), a mount, a bevy of different equipment options, and something like 55 different skills - because that player -wanted- that kind of detail. And they're both very effective in their domains, and play off of each other well.

That's the thing that really sticks out to me about GURPS - it's very playable with a very minimal ruleset (GURPS Ultra-Lite is free, and 2 pages - http://www.sjgames.com/gurps/books/ultra-lite/), and can seamlessly expand when you want more detail. And not only are there a lot of options for that detail, they also show their work - so if you're still missing something, you can generally still come up with reasonable rules. It just gets a reputation for being super complicated because the people who discover it tend to get excited and throw everything in...