It's been a while, but there are a few good things worth downloading.
1. My current free-to-play addiction is Marvel Puzzle Quest. I tried it when it first came out and found it a little too heavy on the FTP side, with too many hooks that made you feel bad for not spending money. They've balanced it more now, and I've been enjoying it for about two months straight. There's constant content, and the concept itself (match-3 combined with combat, combined with cheesy Marvel dialogue) works pretty well.
2. I'm also playing Quiz RPG regularly. This is made by the people who make Puzzles and Dragons, the only other FTP match-3 I play these days. Quiz RPG is basically Trivial Pursuit meets Pokemon. You bring a pack of five monster/spirits with you into combat, and each correct answer to random trivia questions allows some of your monsters (depending on their colors and abilities) to attack. It sounds simple (and the questions are typical Trivial Pursuit ones, ranging from "legit" trivia to things that are killer hard), but there's the wacky Japanese Monster stuff, so there are thousands of potential spirits, and you can (and have to) combine them to level them up, and some spirits are best sold, while some are better as fodder for other spirits, etc. And there are multiple systems, plus a ludicrous amount of new quests (there's a Steampunk Wizard of Oz one now), all of which offer limited-time spirits. Plus daily login rewards and all sorts of other stuff.
3. HalfBrick, who make some of the best iOS games, has made everything they have free for now (I'd expect this'll go away soon). At the very least, grab Jetpack Joyride (a fun endless flyer game with zany missions), Colossatron: Massive World Threat (the best game about a giant robot snake), Fruit Ninja, and Fish Out of Water (a great time-killer involving flinging fish). All do have in-app purchases available, but all are pretty complete by themselves.
4. Damn Little Town. Imagine Carcassonne, but with demons who try to kill your meeples. No online multiplayer yet, alas.
5. Jupiter Jump. The second Flappy-variant game from Noodlehead (they also did the amazing Flappy Golf, which I've mentioned earlier and you should still get; I think it's one of the best free apps in the store these days). This is a quicker and more frenetic game in which you try to nab as many points on the planet Jupiter before crashing into something. A good quick game for fans of action/twitch stuff.
6. Zombie Gunship Arcade. Another Flappy Bird riff, this takes the original idea of Zombie Gunship and distills it to a game where the same control both sends your chopper up, and fires missiles at the ground. Not killing civilians while also managing to stay in the air is the goal here.
7. Metal Slug Defense. A defense game (not a tower defense one) with the Metal Slug assets. Surprisingly fun. Army of Darkness Defense remains my favorite (also free) game in this genre, but this is still fun.
8. Dwarven Den. A fun puzzle game from Backflip (who make that AoD game), with some nifty puzzles, good resource management, and some crafting elements. The FTP hooks can occasionally hit you, but you can always farm some of the lower levels, too.