Lingotopia by Tristan Dahl and Aryo Herwastho
You'll already find an entry for Lingotopia if you search way back in the Free Games archives, but it's just been updated with more of the city to explore, and with additional phrases and words to pick up in a variety of languages. It's an ambitious (if, for now, still a bit limited) learning tool that puts you in a city where you can walk around in third-person, examining objects to learn their counterpart words in a language of your choosing, and chatting to citizens to engage in various quizzes. As you go, words will be added to your vocabulary, hopefully improving your ability to speak and read in, for example, the Norwegian language.
Roaring Streets by cottontrek
Made in just two days for the Game Maker's Toolkit Jam, the impressive Roaring Streets is a sort of turn-based, puzzley roguelike, with a gorgeous visual style—look at those turn-based raindrops!—and a novel, noir setting that plays off that stark aesthetic remarkably well. You're battling behatted ghosts here, something you achieve by moving in range and firing one of your colour-coded guns. The only way to defeat, for instance, red ghosts is to fire your similarly hued weapon. However, you can't change arms at will—that will automatically happen after you walk a certain number of footsteps—so you have to be strategic, in order to remove every enemy and move along.
Necrosphere by Cat Nigiri
In this solid Metroidvania, you're denied your primary tool for getting around in the genre: your ability to jump high in the air. Er, a platformer with no jumping? How on Earth would that possibly work? And, as turns out, it can work surprisingly well. While you can't leap at will, you can ascend by running into little boingy bubble things, which crop up as you trot about. There are also levitation fields that will allow you to hover upwards, and probably other clever devices lurking about. It's a fairly big game, this—probably bigger than you were expecting—that is no less satisfying for your inability to leap at will.
Anatomy Attack by Dave and Dex
Here's a top-down, twin-stick shooter set inside the human body, meaning you take control of a single cell fighting off infections (by shooting them with, well, I have no idea what those bullet-like missiles are supposed to be). OK, I say single cell, but as you clear out each room you're given the option to acquire a few helper cells, who will follow you about, shielding you from harm, or seeking out enemies of their own volition. As you progress through the game, you'll gradually build up a posse of defending organisms, and that's a neat way to handle power-ups.