Opera Mobile will off a PC like browser experience to your Android device. They are working closely with phone manufacturers to have this app preinstalled on upcoming Android devices. In the meantime they are looking to improve on their current Opera Mini offering with the new 5th edition. It's currently a beta but you can try it out now if you like.
Currently Opera Mobile 10 is available for beta testing but isn't ready for Android yet. This app is expected to launch sometime towards the end of the year and will have major competition in the form of Mozilla Firefox offering. Unlike Opera Mini, Opera Mobile doesn't go through servers to get information, the information is gained directly through the device itself. For a program that's pretty much in alpha stage, it runs pretty well.