Apple has approved third party browsers for iPhone. These however seem to be more or less a different UI for the same browser engine as the Safari browser that comes with iPhone. They are like version 1 of a browser with many shortcomings.
It will be interesting to see if Apple will allow "true" third party browsers like Opera on iPhone. The included Safari browser is already the best mobile phone browser.
For more details on the new iPhone browsers, check out this PCWorld article.