A quite fun free PC game: Beret. It's a puzzle-platformer, more puzzle than platform. There are occasional moments of careful jumping, but the game's single keystroke "save this position" and "restore that position" mechanism removes the bulk of the horribleness of "timing puzzles". Also a backup "restore the saved position before that" option for if you accidentally save in a deathly precarious position, and always the option to just start a room again. Pleasingly, all these things also rewind the time, so you're allowed to rewind as much as you need to for the speed challenges, should you decide to do them.
Also fun is that a level's speed challenge (running from start to finish) is frequently around 45 seconds, but doing all the other subtasks (kill all monsters, collect 100 small easy fragments, collect 4 medium difficult fragments, and collect 1 large extra-difficult medallion) is more like a ten minute task per level. Since you only need a subset of medallions to move on, you can mostly play in your preferred style - good design there.
This was recommended by the Caravel Games Newsletter - it's not one of their games, but it is kind of like a platform game version of their DROD series (or this link includes the free, oldest one), which I also partially recommend (I don't recommend the RPG one).