Epiphany is a Free web browser for Unix-like systems, designed to be a lightweight, easy-to-use browser conforming to the Gnome Human Interface Guidelines. The project was started in 2002 as a fork of Galeon by Marco Pesenti Gritti, who originally created Galeon to be an easy-to-use browser with better integration with his Gnome desktop than the Mozilla project. Over time, Galeon grew mountains of features and preferences, targeting power users rather than his original goal of simplicity; forking to create Epiphany gave both camps the freedom to create the browser they wanted. Epiphany is now the official browser of the Gnome desktop, although every distribution I'm aware of uses Firefox by default at the moment. This is kind of a shame, but it's probably inevitable given the recognition Firefox has among normal people. (It turns out that work on Galeon has now pretty much ceased, with some of its features being brought to Epiphany as extensions. This is probably good news from the point of view of reducing duplication of effort.)
Epiphany's bookmark system is worth mentioning. Rather than providing a folder hierarchy in which to arrange your bookmarks, you assign them to tags, rather like del.icio.us. (There's an extension to sync these tags with various social bookmarking sites, if you're into that kind of thing.) If you put a bookmark into the magic Search Engines tag, it appears in a drop-down list below the address bar; typing some text into the bar then choosing one of the bookmarks causes the string %s in the bookmark's URL to be replaced with the text you entered. For instance, I have a Search Engine-tagged bookmark for http://everything2.com/e2node/%s, giving me easy access to any arbitrary node directly from the address bar.
Traditionally, Epiphany has used Mozilla's Gecko engine, just like Galeon, Firefox, Seamonkey and friends. As of recently, you can choose instead to use the Gtk port of WebKit (the HTML widget from Apple's Safari browser for OS X and Windows, which is a fork of KHTML from KDE's Konqueror browser, which was built on the QT toolkit, Gtk's main rival – confused yet?), which some people believe to be smaller, faster and cleaner. There's talk of making WebKit the default layout engine in some future version of Epiphany, but (having had a play) it's just not good enough yet.
Over time, Firefox has started to fit in better with your environment, so it could well be that it's already Gnome-y enough for you. But Epiphany is better-behaved and does everything I need to do without having to install a mountain of slightly broken extensions from mozdev. Assuming you don't want your browser to do the laundry and make your coffee, you should give it a try!