Have You Played... N?
v2 is great and still free
Have You Played? is an endless stream of game recommendations. One a day, every day of the year, perhaps for all time.
N consumed me. For months, for hours a day, I'd be poking at arrow keys to perfect jumps, wall-jumps and slides in order to dodge electrifying scooters, crushing thwumps, explosive mines and laser-targeted missiles. My reward: a replay at the end of each exhausting level which discarded my failed attempts and left only the perfect, graceful, balletic triumph.
N had hundreds of levels, back then. v2.0 has hundreds more and it's still free.
Returning to it now, it strikes me how weird N's movement physics is. You feel heavy, but pick up horizontal speed rapidly even via air-control. You're heavy and slidey at the same time, making it hard to get height but hard to pin your feet to small platforms.
But stick with it, because soon those quirks of physics become a stage for your growing mastery. The likes of Super Meat Boy and VVVVVV have done it since, but N was the first platformer that tipped me into the pursuit of perfection.
It's also, like all of them, a game that reminds me that I'll never reach it. N does that more swiftly than most by offering a leaderboard where every quick time - all of them quicker than me - can be clicked in order to watch a replay of the run. That route you found around a particular obstacle will be revealed as just one option of many, and there's as much fun to be had as a spectator of other people's death-defying leaps and bounds as a performer of your own.
Try also the user-made, no-hands levels, which pinball your character around the single-screen rooms like a circus performer while you don't need to press a single button. Lovely thing.