We all have game challenges that we either want to or have done. Post them here. I'll start. Fire emblem but you can only use 3 classes of units for the entire run and everything else you will have sit out. Sonic but you are alloted 25 jumps per level. No hit runs for various games or levels.
I don't know how much of a challenge this is, compared to what I've seen other people do, but what I've been doing in Breath of the Wild is not buy any clothes. I could only use the clothes I find or are given to me. It's more than possible, but it's made me play the game differently than I normally would.
The most common type of challenge that I've done is speedrunning. This comes in many shapes and forms depending on the game and category. Personally, I have tried my hand at Mario Kart Wii (all tracks) and Donkey Kong Country 2 (all levels, no bonuses). This is also a frequently done challenge, but the Ocarina of Time randomizer challenge is one that I did recently. It was thoroughly enjoyable and funny at times, even if the game wanted to make me work as hard as possible for it. As for more personal or self-imposed challenges, I like doing the Ironman challenge in Fire Emblem. This entails putting the game in classic mode (if necessary) and never resetting. The challenge is akin to how you're supposed to play the games, but the rules ensure that you NEVER reset regardless of what happens.
Speaking of challenge ideas, here's one that I haven't tried before: Pokémon but you ban a random type per gym/trial (or per episode in the case of episodic games like Reborn or Rejuvenation).
One ban at a time is... cyclic, right? Here's what I'm thinking: Let's say I ban normal-type mons from start up to the first gym. After getting my first badge, I can use normal-types again but now banning fairy-types until the second gym instead. That goes on until the last type ban lasting from the moment I get the 8th badge until becoming a champion.
If you have Super Mario Maker 2, challenge yourself to make a stage using only enemies, settings, and items that appear in your chosen theme (so no Magikoopa in Super Mario Bros, for example--you are limited to only things that were in the original Super Mario Bros.) Make your level feel like it could be in the real game!