Demo videos taken by a member of AndroidForums show an early version of Mozilla's mobile browser, called Fennec. Keep in mind these are very early builds, and that the finished product, when released, will likely be very different from what you see can see below.
Martin Schirr also put together a website to show you how to install this on your own phone (given that you run Android 2.0 or later.) He runs it on his Milestone, so for those of you who will try it on other phones, good luck! I hope you guys know German, I know the other side of AndroidPIT does :D
Here are links to the two videos from his post on AndroidForums:
Fennec for Android on Motorola Milestone
Fennec for Android on Motorola Milestone Addons
Other Sources: AndroidForums, AndroidCentral, AndroidGuys
Image from AndroidGuys