It might be just coincidence, but I felt like checking the Opera web browser site today - something I do only rarely. By chance, they've just released version 8 of my favourite browser to the world yesterday (Windows and Linux versions, Mac version in beta) so of course I just had to go get it. I've been using it for a year or two (ish) now and although I occasionally switch to Firefox/IE (when in Windows) when I have to, if I could live in Opera I would.
For the majority of people reading this, I suspect you'll be using Internet Explorer, maybe Firefox. If it's IE, where have you been? Do you really like millions of windows open on your desktop, one per page? Everyone else has tabbed browsing. Opera does it well. Your browsing will be more secure with Opera (count the IE hack exploits). It has a relatively small market share but I don't understand why it isn't more popular. Ok, it's advert-supported but you can pay to remove those if they really take up too much screen space (and they don't use much). Firefox might render and work with more pages, but it's just so lacking in customisation and it's not as fast.
For Linux (KDE in particular) users, Konqueror is pretty fast and will render uncomplicated pages fine, but it does fall down on too many sites to become anyone's full-time browser.
Opera is multi-platform, fast, very customisable (find a toolbar button you don't want, or one you want elsewhere? change it. prefer to move back and forwards in your page history with the mouse? you can (guestures). got a key shortcut you want to use for anything? set it up.); and I also rather like their bookmark/history/search/transfers-list (like firefox's download manager) sidebar that you can bring up/shut down with F4 (or any key you change it to), it's search-as-you-type is great.
One of their big features (but not one I care about) is support for different devices - they make a version for your PDA/smart-phone, and for quite a few other types of computer too. It's also really easy to zoom in/out, and it zooms images too. Set up your own stylesheet for it to render pages with and it'll ignore the page's own, or combine them.
In short, it's great. If you've not given it a go before, why not take a look.