Opera Software CEO Jon Stephenson von Tetzchner told NY Times that Apple isn't allowing them to release a version of the Opera Mini browser for the iPhone, because Apple doesn't want competition for its own Safari browser:
Mr. von Tetzchner said that Opera’s engineers have developed a version of Opera Mini that can run on an Apple iPhone, but Apple won’t let the company release it because it competes with Apple’s own Safari browser.
Opera Mini is free, and can be downloaded onto many phones. The company earns money, as it does for its computer service, from search engines. In addition, some carriers pay Opera to develop custom versions of Opera Mini for their systems.