It's actually quite hard to truly escape Internet Explorer or Firefox, because many alternative browsers just wrap a different user interface around the same rendering engines that drive the market leaders.
Then there are the browsers that build upon the Mozilla rendering engine (Gecko), which also powers Firefox. Flock concentrates on the social side of browsing by integrating with del.icio.us and bringing drag-and-drop blogging by way of a right-click Blog This tool. Adding comments to MySpace or LiveJournal is easy, too, as is posting images to Photobucket or Flickr. The Search tool is great, too, giving an overview of hits in your bookmarks and history, as well as the web. Of course, you can do most of this with Firefox and some extensions, but if you're into the social side of the web, it's one to consider.