Considering that the iPad is as much of a browsing device as it is an application platform, you'd think there would be many alternatives to Apple's Safari, but thus far no other full-featured browser has shown much of a presence.
Opera Mini can be used on the iPad but was really developed for the iPhone. Firefox has a history and bookmarks app on the iPad, not a browser. But neither offers much in the way of iPad-specific features.
Lunascape, with its "iLunascape" browser for the iPad, focused specifically on how people use the tablet device. It reconfigured the browser UI, taking into account how people hold and interact with the device. For example, since you often hold it from the bottom, it has moved most actions down to the bottom of the screen. It termed it "In Reach Interface."
An important part of the interface design is the introduction of tabbed browsing--common in standard desktop browser but not in mobile-device browsers. The company suggests that tabs can become an important aspect of tablet browsing and claims that switching tabs is easily done via thumb taps.
As a side note, the Japanese version of iLunascape, released in Japan last month, was ranked No. 1 in the free-application category within the 24 hours of its release. Clearly, there is an interest in alternatives to what Safari provides.