The web browser built in to Android 4.0 Ice Cream Sandwich rocks. It's so fast and stable that it easily beats out any of the third-party alternatives, and new features like a Chrome bookmark sync, built-in full screen and a Desktop mode mean you won't need the extra features in apps like Dolphin Browser HD. But even the best can be improved upon, and thanks to Android's open-source nature, it has. Browser+ is now available for free in the Android Market, building a few handy extra features into Ice Cream Sandwich's built-in browser.
Naturally you'll need to be running Android 4.0 in order to use Browser+, because the API calls just won't work with older versions. That said, it seems to be working just fine on my Galaxy Nexus with an extremely unofficial CM9 branch, so it cross-compatibility shouldn't be a problem. The two primary additions in Browser+ are an expanded quick-launch menu, more in line with the one found on Honeycomb tablets, and an selection uof user agent strings. These are far more generous than the "request desktop site" included by default, and range from the standard Android, desktop, and iOS modes to Honeycomb or Nexus One Froyo. Very handy for the web testers out there.
The app doesn't require root, so as long as you've got ICe Cream Sandwich you're good to go. Developer Beansoft is taking suggestions for new features in this XDA post, so if you've got an idea, go ahead and send to him. (Fun fact: this is the same developer that makes Thumb Keyboard, my absolute favorite Android virtual keyboard!) For more ICS app mods, check out the enhanced homescreen NovaLauncher.