I am a fan of the Android web browser; I find it to be almost as good as the browser on that fruity phone. The only common complaint about the native Android browser is multitouch– more specifically the lack thereof. I suspect that Android is going to go multitouch for real, but meanwhile a new browser steps in to fill the void.
Dolphin is a free browser that looks a bit like an ugly duckling, but users report it works pretty well. It has the usual requirements for a serious web browser — tabs, gestures, RSS integration and of course, multitouch. It is in the Android Market so if multitouch is what you live for, go get it.