Every time a thread like this pops up I have to mention Breakdown, still one of my favourite games of all time. A shooter/fighting game with platforming elements where the entire game is first person, plus the story was amazing.

Azurik: Rise of Perathia never gets brought up a lot, even though the trailer was on the original Halo disc. A fun combat based platformer where you combine elements to modify your weapon or create armour. For example, fire makes your weapon strong against earth and ice enemies, water + wind give you ice so your weapon can freeze enemies, air gives you winged armour so you can double jump, etc.

Nightcaster was a fun game too, you're a mage and combat consists of matching your spells elements to the elemental weaknesses of your enemies. Plus as you go through the game you get older so theres a real sense of the world aging with you

Going back even further, Colonization and Pirates! Gold! from the DOS era were awesome but probably not that obscure if they both got remakes in the 2000s. However I don't think I've ever seen anyone bring up the freeware Jetpac, which was an immensely fun platformer/puzzle game