There are a lot of browser options out there for Android, but one from the "old guard" of desktop browser publishers is Opera Mini. This one's been around a while (longer than Android itself, in fact) but recent updates may merit another look from those who have passed over it before. Version 7, released just today, includes a bevvy of new features such as an improved compression engine, hardware acceleration on certain devices, and support for Ice Cream Sandwich's Android Beam. You can download the updated browser for free in the Google Play Store.
Opera Mini's compression is what distinguishes it from other mobile browsers - requests for websites are processed through Opera's servers, then the servers send your phone a reworked and optimized version of the HTML or CSS page. This feature's called Turbo, and now it includes the ability for device-side hardware acceleration to add to the compression computation and performance. Interface tweaks to make the browser compatible with Ice Cream Sandwich and the Beam function of Android's default browser are combined with a reworked Speed Dial start page.
There's still a few things holding Opera back. Its customized rendering engine still has trouble on a small but considerable number of websites, owing to Opera's still tiny share of the desktop browser market. And while Opera Mini includes a lot of features that others are just now catching up on, such as the ability to sync bookmarks between mobile and desktop, it still can't use popular plugins like Flash. But if you're a regular Opera user on the desktop or any other platform, odds are pretty good that you can look past these foibles.