Other Google apps are available for the iPhone, including the built-in Maps and YouTube apps (see note below). The Google Mobile app and Google Earth are available in the App Store. Google is the default search engine for Mobile Safari. There have been rumors that Apple is considering making Bing the default search engine for a future version of the iPhone OS. Also, don't forget that Apple bought a mapping service company, giving rise to rumors that "Maps" might not continue to be powered by Google
Then again, if you took a grain of salt for every rumor you heard about Apple, you'd probably die of hypertension.
Getting back to Opera for the iPhone, I hope that it will be approved. There are other Web browsers, such as iCab, available for the iPhone, but all of them use WebKit, which means that you are getting the same browser, just with a different user interface. Opera is a completely different rendering engine. I have some concerns about Opera's model. For those who aren't familiar with it, Opera sends all Web traffic through their proxy, which reformats the page and sends a streamlined version to the phone. As someone who spends an unfortunate amount of time in areas with only AT&T "EDGE" coverage, Opera sounds very enticing. That said, as soon as you start talking about "https," security and privacy concerns quickly come to the forefront.
Assuming that Opera can address those legitimate concerns (or did before it was submitted), Apple should approve it. Then again, Apple should approve Google Voice (and certainly should not have removed existing Google Voice apps). When the iPhone SDK was announced, it came with a very limited set of restrictions regarding what types of applications would not be allowed. Users and developers were presented with what sounded like a "Default Yes" App Store: "As long as your apps don't violate any of these things, it will be approved." There was, however, one additional word after all of the specifics: "unforeseen."
Turns out that "unforeseen" covers apps that "duplicate functionality," provide "limited functionality," or seem like they may compete against Apple in an area where competition is not desired.
While I have some specific hopes for what Apple will announce as part of iPhone OS 4.0, my larger hope is that the App Store process becomes a lot more stable. Once an application is available, it should almost never be "pulled." Users should have the choice of which browser to use, which calendar app to use, and which mail program to use (almost three years later, we're still waiting for a unified Inbox; a competitor could have gotten us a mail client with that ages ago).
UPDATE: As mentioned in the comments, the Maps and YouTube apps were not written by Google, they were written by Apple using the Google APIs. Also, given the announcement today about background location apps, it sure would be nice to have a Google Latitude app instead of just a web page.