A peaceful journey through the cosmos, Run is elegant in its simplicity. You, a small grey creature, are running along a series of platforms, using the arrows to move right or left and the spacebar to jump over gaps. Go far enough to either side, the wall becomes the ground. If you fall into a gap, you fall into space and have to start over.
This game was a key part of my youth. It was the default game for us to play on school computers when we didn't have anything else to do. Though I can pass all the levels easily as an adult, it's still a fun game if you haven't played it before.
Run's sequels, Run 2 and Run 3, don't stray from the formula too much. The second game places you on a series of 3D blocks rather than flat walls. The third places you inside a cylinder with temporary panels that fall away after you run on them. They are, however, significantly harder. If you've finished the first one (or find it too easy), the second and third may be a suitable challenge. The second even has little glowing orbs you can collect for extra points.
There's no shooting, no battles, no blowing things up. Far from the intergalactic power trip of games like Star Realms, it's not about points, tech or territory. It's just you, the gaping void and what little solid space stands between. This could be a metaphor for something, but I'll leave that part up to you.
While the game has electronic background music, I often like to turn the music off and play something else or listen to the radio. 'Run' isn't a rhythm game, but music improves the experience and can create whatever atmosphere you'd like. A search for 'ambient space music' may help you find something particularly thematic.
If you're looking for a challenging and peaceful game with a simple concept, Run may be for you.
You can play the games in the Run series at Cool Math Games.