
Noitu Love
You are Noitu Love, an eight-year-old boy with super speed and strength. You must fight Dr. Darnicus Damnation's army of grinning goons, the Darn robots! Looks like MegaMan, plays like Streets of Rage. This is an action game with huge explosions and awesome music, and is an excellent way to burn off some latent aggression once in a while. It also has some really fun bosses (especially the last boss). Noitu Love 2 was also released less than a week ago, but you have to pay $20 to get it. The demo is even more badass than the original game though, so I think it'd be worth it...

Bonesaw
You play as a hockey player, whose team has been kidnapped by an evil ref (placed into an interdimensional penalty box, no less), and now you have to run around platform levels fighting the enemy team and wild animals for some reason. The game copies aspects of the old Kirby games (especially the bomb blocks, which are actually quite well implemented) You also have a "Bonesaw" meter, which fills up whenever you fight, and every so often you get to unleash the Bonesaw. Oh man, the Bonesaw. Bonesaw just kills everything. Bonesaw... is ready. The game has horrible slowdown on some computers, so be careful!

Alex's Adventure
Conventional if slightly surreal platform game. Not a huge amount to say about this one, it's worth a try if you still wish there'd be a sequel to Lyle in Cube Sector. Some cool puzzles, a bit short though.

Darkside Adventures
Mario-esque platform game with a rich game world (and an excellent protagonist & NPC roles) which I enjoyed playing. Pretty straightforward. You are the arch-chancellor to the King of Imps, who is one day summoned from his vacation by the king to find Princess Daffodil's crown, which she lost during a rousing game of hide and seek. Too bad your inane quest is impeded by an altogether larger plot involving the "Faraway Star"...

Spud's Quest
Ostensibly a Dizzy fan-game (it even has a cameo of the guy), this is an inventory-oriented platform game where you have to walk around picking up items, using them on things to get other items, etc, etc. Faithful to the original Oliver Twins games without being derivative (okay, maybe a little bit), definitely worth playing if you like Dizzy. If not, well, this probably won't change your mind.

Barkey Shut Up and Jam: Gaiden
The year is 2046. Basketball is dead. You are Charles Barkley, once a famed NBA player, now destined for a life of shame and guilt living in the slums of Neo New York after causing the apocalypse with your Chaos Dunk. But then... a new Chaos Dunk is performed, and Barkley is assumed as the culprit! And Michael Jordan himself is leading the witchhunt! ohhhhhh nooooo... This game considers Space Jam part of its canon and is chapter one in the Hoopz Barkley saga, and is composed of equal amounts basketball trivia and JRPG satire. If nothing else, you can spend many happy hours playing "spot the ripped sprite" as you play through the game. There is a sequel in the works (albeit with a different programmer), which may even rule as much as this game. Don't worry if you don't know anything about b-ball, I don't and I thought this game ruled. It's a ridiculous scenario but played completely deadpan, but with just the right amount of silliness in the dialogue and game events.

Iwanaga
Alien Soldier clone set in feudal Japan. Really badass, great graphics. (too bad I couldn't take a screenshot, though I stole one from another site. sorry, other site)

Yume Nikki (Title translates as "Dream Diary", allegedly)
This is the game I've been posting random screenshots of in the Queen of Jellybean thread. In this game you play as a young girl who spends an unhealthy amount of time asleep, and you wander the corridors of your mind while asleep, searching for "effects". There is some REALLY fucked up and terrifying stuff in this game. It kind of plays like Flimsy's Town of ZZT, which means I love it. It's almost unnecessarily impenetrable at first, but stick at it and you'll reap the rewards. (Tip: get the bicycle from the "funny floor" area, it's directly left from the entrance)
Please add to this thread with your own recommendations! You don't have to add screenshots, but a description as to why people should want to play it would be a Good Idea