Apple seems to have changed their policies and is now allowing web browsing applications on the Apple App Store.
A couple of new applications are now available which provides an alternative to Apple Safari on the iPhone and iPod Touch.
These include:
Edge Browser
Incognito
WebMate:Tabbed Browser
Shaking Web
It is not clear if any of these applications are using their own rendering engine. It seems highly unlikely.
Opera Software had recently said that they had a working version of Opera for iPhone. It is not clear whether they would be allowed to make available Opera Mobile on the Apple App Store.
