Major reneg on my comment about the weaksauce browser in IM+. The browser contained in the new update is pretty functional. It has back and forward buttons now, as well as a refresh button (whereas the last version of it had none of those things). A visit to thismachine.info revealed that the browser in the program is Mozilla 5.0. This is not the only instance of Mozilla on the iPhone, though it is one of the most functional browsers using the Mozilla code.
Many applications for iPhone have minor browser functionality built in, though minor usually means it will load content within the program, but there is no way to freely browse. The TweetDeck iPhone program, for example, allows you to see links on Twitter via a Mozilla-based browser, but not only are there no forward or back buttons, but there is not even a field for entering a URL.
It’s hard to say whether IM+ was able to add a functional, non-Safari browser because Apple is getting laxer with its policies, or if someone was just asleep at the wheel for this update’s approval. The former seems like it might be verified by the existance of other iPhone apps such as FullBrowser, which is a semi-janky browser made from Mozilla 5.0 (though it does have tabs). That said, some other web browsers in the App Store seem to have been pulled after being released, which suggests that Apple still wants iPhone users exclusively running Safari.