Back when a character with amnesia was a compelling plot device, Flashback ruled the narrative-platformer roost. I played it on the Amiga in the mid-90s and thoroughly enjoyed the experience, but it was developed for multiple platforms by Delphine (and later for even more by Tiertex.) You play as the memory-challenged Conrad who has crash-landed in a jungle after a high-speed hover-bike chase and needs to figure where he is, who he is and what the hell is going on.
Of course if you watch the trailer for the remake of Flashback it will tell you exactly what is going on, because it spoils around half the plot of the game. Not a big problem if you’ve already played it, but a bit crap if you’re coming to it fresh. Don’t watch it if you want to keep some of the narrative a vague secret.
The remake will set you back $10.00 USD / £8.00 GBP, and there is a demo out there on Steam if you want to try that first. While the trailer is very spoilery, it does at least give an indication about some of the new bits and pieces added as well. So if you already know the story it’s worth it for that.