Cro-Mag Rally [iTunes link] -- I used to play this on the older PPC-based iMacs and it was also an early entrant to the store. Cro-Mag is cute but it also plays exceedingly well. If you want something like Mario Kart on your iPhone, this is about as close as I've found. For a quick racing game that nearly anyone can enjoy, Cro-Mag is a true iPhone "classic."
MotionX Dice [iTunes link] -- You never know when you're doing to need some dice. Plus, MotionX gives this app away, and it's a beautiful example of what can be done on the iPhone. When someone wants to "see something" on my iPhone, often I'll show them how the shadows cast by the dice change as I move the iPhone. Then we'll play some dice games.
Flick Bowling [iTunes link] -- There are faster, cheaper versions of bowling on the iPhone. I find Flick provides just enough eye candy and immersion to suit my taste. Plus, it loads pretty fast and you can get to bowling without a lot of setup. It's a casual game that looks bigger than it is.
Dizzy Bee [iTunes link] -- One of the big, early hits for the iPhone, in no small part because the super cute free version moved a lot of units. Dizzy Bee is the app everyone seemed to give to the kids to play with, but the challenges get pretty tough. Like any great game: simple to learn, hard to master. Plus, there's now a sequel.
Keep reading for some games that are a little more under the radar and some genuine iPhone essentials...