Is it possible to connect two iPhones over the web (wide area network) for a real time gaming experience? Would the connection be fast enough for a game (for example) like pong? What steps should I take? What type of objects int the iPhone SDK should I employ to make this happen?
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Yes, the iPhone can communicate with the web. You're going to run into the same issues as desktop clients though, including intrinsic network latency and NAT traversal problems. Additionally, you're going to deal with standard embedded systems problems, i.e. you can't tax the CPU and expect network performance to stay high. The solutions are the same as those on the desktop, e.g. having a central "game server" that mitigates the NAT traversal issues and moves "hit" determination away from the clients.
If you want to bypass the web, check out Whiteboard, although not a game, uses a device's wifi connection to collaborate in realtime, with very low latency. I think that if you can figure out how to make your game connect to another's device like that, you could pull off some quality gaming ideas.
At least, that's one of the things I want to do.
If you need to game over the web, you're not going to easily get around the problems @John Douthat mentioned above. For games like Go (see Tetsuki for an example) and Chess, that's not a problem, but a shooter (obv) would be.
And, no, I have no affiliation with Whiteboard (or Tetsuki for that matter), I just think the tech is cool.