Okay, so this turned out to be a rather large list. Best just skip the formalities and get right to the good stuff.
Arm Wrestling Evolution - AWE - We have every reason to love "extreme" boxing games. It's like an instinctual thing. But take the general concept of over-the-top characters, an awesome art style, special moves, and combine it all with arm wrestling? That's attention-grabbing on a whole new level. Also, my apologies for the pun. I swear it wasn't intentional.
The Simpsons: Tapped Out - A city-building game featuring The Simpsons. Yeah, this totally won't get a ton of attention. Still, I think it's more than worth a mention. I mean we get to build our own Springfield. And interact with characters like Apu, Homer, Bart, etc. I can only imagine how many downloads it's going to get.
Sky Settlers - Okay so it's yet another city-building game (of a sort). That doesn't mean it's not without its charm. I mean, building a floating city in the sky is cool. And it's got a nifty cartoon art style. Plus it's free and all that.
RPS Rumble - Melding puzzle gameplay, Rocks, Paper, Scissors rules, and garish Luchador masks is so ridiculous it's borderline genius. It's not exactly bursting with free content, but what's there is more than solid enough. And it can keep someone busy for quite a while depending on their personal skill level. Plus it's goofy, and goofy is almost always cool.
R-Tech Commander: Galaxy XD - I know I'm a sucker for sci-fi stuff, but this one honestly looks pretty cool. RPG elements, strategy stuff, armada customization via ship classes and equipment, and a nifty visual style? Yeah, I'm totally sold. Which is even more cool because I don't actually have to buy anything.
Zombie Panic in Wonderland - The bizarre WiiWare shmup has officially come to the App Store. And it's free. I think paying absolutely nothing to blast through waves of disfigured Wonderland denizens as any of seven characters with multiple weapons to choose from is a sweet deal. I mean, who wouldn't think that?
Idonia - So help me I love character customization. So the idea of setting up a 3-person team (with 5 classes to choose from), then finding and equipping them with special gear (lewt drops!!!), and powering them up with special skills is quite alluring. Of course it's also got upgradable weapons and armor. And online PvP multiplayer. It's also free, people.