If you wind the clocks back to the days before the App Store, the closest thing we had to any kind of game (Assuming you weren't in the super-early jailbreaking scene) were very basic HTML-driven browser games. They weren't pretty, but, they worked.
This is what makes Dominic Szablewski's X-Type noteworthy, as it is pretty. Surprisingly so, especially for a browser game. All you need to do to play it is mash this link on your iPhone, and you're good to go. Gameplay is a little simple, and basically consists of destroying increasingly elaborate bosses, but it's really neat when you consider that this is all being rendered inside of your browser using HTML 5.
Dominic has a whole bunch of other cool stuff on his web site, including his Oculus Rift port of Quake, game engines, and a few other HTML 5 games to fiddle with. Be sure to check it out.