I've been using Opera for many, many years and they are constantly innovating. The were the first browser that I know of with tabbed browsing, the first with the speed dial, among many other features. The browser has a built in mail client, which I use mainly for reading RSS feeds, which is nice because it keeps the entire history of the feed, and it also has a built in BitTorrent client, which has been convenient on a few occasions when sites have BitTorrent download links. It supports extensions, but they aren't quite as advanced as Firefox extensions, although from a security standpoint that might be a good thing and installing them doesn't require a browser restart. Opera Link is great for syncing up your bookmarks, history, speed dial, etc with all your other Opera browsers (desktop and laptop for example). Opera Turbo is similar to Amazon's Silk browser feature to use a compressing proxy, although Opera Turbo can actually detect a slow connection and only use the feature when it needs to and then only when it is turned on. I haven't really messed with Opera Unite, but it seems like a pretty cool feature which allows you to basically set up a limited web server on your own computer for sharing files, broadcasting a web cam, accessing your home media library remotely, among other things. Back in the day I had to have another browser on standby because there were many pages Opera didn't work with, now it is very rare to find pages that don't work with Opera, plus Opera supports masking the browser as IE and Firefox for those pages that perform browser checking and tell you that your using an unsupported browser.
If you haven't tried Opera, give it a try, you might be pleasantly surprised at how advanced and slick it is.