Looking for a platformer that'll bend your brain a bit? AlterEgo: DreamWalker is the 8-bit-on-acid sequel to AlterEgo, and basically just builds on its predecessor. More levels, arguably trippier visuals, and the same switch-up platforming action of the original. The game mechanic, by the way, is simple, but fairly novel: you move your character around the platform world, but on the opposite side in a mirrored position as an 'AlterEgo' (the ghost-looking thingy).
The alter ego doesn't take damage and can move through any obstacle, and you complete levels and progress by swapping positions with him at any time. Just watch the video - it'll immediately be clear what's going on.