The NY Times profiles Opera Software, the company that distributes the Opera browser for multiple platforms. According to the article, however, Apple is not allowing an iPhone version of the browser into the App Store:

Mr. von Tetzchner said that Operas engineers have developed a version of Opera Mini that can run on an Apple iPhone, but Apple wont let the company release it because it competes with Apples own Safari browser.

Gruber speculates that it could have to do with the Javascript interpreter or, more clearly, that Apple has been restricting apps that compete directly with some of their built in iPhone apps such as Safari.

Apple has been criticized for its decision to restrict certain applications from the App Store, and this suggests users shouldn't expect any other web browser alternatives (such as Firefox) to appear in the App Store at any point in the near future.