The OSR movement (the Old School Rules/Revival/Renaissance, etc.) has, over the years, brought to light a lot of interesting rules and ideas, but a recent instance, namely Bill King's One Sheet Rules, seems well worth the time to consider.
Taking inspiration from early editions of D&D, The Black Hack, Knave, and other OSR and rules-light systems, the One Sheet Rules are an ultra-light, flexible system that takes many familiar OSR concepts and shapes them into a compact framework that would be just enough for any OSR style adventuring.
The simplicity of One Sheet Rules is outstanding. For example, almost every step in character creation is an easy to remember rule of "three": three points go to three abilities (STR, DEX, INT), you begin with 3d3 hit points, you choose three items of equipment or spells, and so on. The basic system, roll d20 and roll high against a target, is cleverly configured so that, if you choose, only players ever need to roll. To run an encounter, all you need to know is the level of the opposition, which serves rather like the HD rating of older systems. There is a experience system, but "advances", like experience rolls in RuneQuest, are based on rolls, not accumulated experience points.
Is it perfect? No. But it is imminently adjustable, and that's what matters. Personally, I would give characters slightly more hit-points in the beginning, like RuneQuest, but with a flatter accumulation and a maximum of about 18. And I would decouple Monster levels from hit points, so PCs could face a frail but deadly-swift foe, or a weak attack from a massive creature that takes considerable damage to drop. But both of these decisions are but a moment to make and easily ported to the rules.
With the Once Sheet Rules, it's possible to convert adventures and even whole campaign settings on the fly. I've sometimes wondered what it would take to pick up and run an old MERP adventure or start playing in the Old World or Warhammer without the cumbersome original rules. Although Basic Roleplaying is always an option, ultralight systems like One Sheet Rules are even faster to adapt.
Where to find them
The One Sheet Rules by William King are available on itch.io: https://billk.itch.io/one-sheet-rules
You can also subscribe to the One Sheet Review mailing list (links in the rules), which allows you to receive the One Sheet Magic and Monsters edition, which includes a basic bestiary and spell list (highly recommended).