Earlier this week, there was a sudden influx of web browsing applications in the App Store. Mac Rumors points out that some of them, most notably Edge Browser [App Store link], have very old release dates even though they only showed up in the store recently (Edge Browser's release date is listed as Oct. 13, '08). It's important to note that these aren't true third party browsers, but enhancements to Mobile Safari.
What's interesting is that Apple has previously rejected applications for "duplicating functionality" of some of their own software. Specifically, Podcaster was rejected because it "...duplicates the functionality of the Podcast section of iTunes," while MailWrangler was denied for duplicating "...the functionality of the built-in iPhone application Mail without providing sufficient differentiation or added functionality."
Perhaps Apple is now loosening the reigns a bit. Applications like Edge Browser, Incognito [App Store link], QuickSurf [App Store link] and WebMate: Tabbed Browser [App Store link] offer web browsing functionality in one form or another. For example, Incognito allows for history-free browsing, QuickSurf speeds things up by omitting most images and WebMate queues up all links for later viewing.
Sure, they aren't full fledged, third party browsers, but it's baby steps we're after.