My favorite feature in Opera is its multi-document interface. Internet Explorer's idea of a multi-document interface is having a taskbar button which contains all 7-or-so windows where you have to do extraneous clicking to get anything done. Internet Explorer really isn't tuned for heavy browsing, it only tries to be by "sweeping things under the rug", I guess you could say.
Firefox's implementation of multi-document browsing is stronger than Internet Explorer's but it is still weak, considering that there is no ability to minimize/maximize/resize individual pages; Firefox has a tabbed viewport and isn't designed for multi-document browsing.
Opera, on the other hand, allows you to work with multiple documents inside a single window and minimize/maximize/resize individual pages. Navigation is extremely effecient: hold the right mouse button and click the left one to go backwards and the opposite for forwards, holding down the right mouse button and scrolling the middle wheel allows you to easily switch between documents (in other words, you don't even need to move your hand in order to navigate all of your favorite sites). Not only that but you can grab a page by it's tab and drag it off of the interface and into it's own window. Nothing currently available beats Opera's multi-document interface.
My next favorite feature is the zooming capabilities; again, nothing beats Opera's implementation. Internet Explorer and Firefox have a hard time getting text to be bigger or smaller. Opera zooms in on pages like they were being brought closer to your face, everything is zoomed. Not to mention how much easier it is to zoom in Opera compared to other browsers. To increase the text size in Internet Explorer you have to stop typing (if you're typing a reply on a forum, for example), grab the mouse, go to View->Text Size->Select and you have to do that again when you're finished zooming. In Firefox you can do the same thing except you can also use Ctrl++ or Ctrl+-, neither which is really easy to do without looking at the keyboard (just look at the position of your hands as you do these, so ackward and hurtful to those with arthritis!), to return back to normal you can use Ctrl+0, which is also very ackward. In Opera you simply press + or - and it will zoom in and out and pressing * will make it go back to normal, simple! Why does Internet Explorer remove keyboard shortcuts (an accessibility feature) for accessing their zoom (another accessibility feature)? Why does Firefox require the control key to be held down, what else am I going to use the + or - keys for in an uneditable part of the browser/page? Opera's implementation of zooming is the only one which makes sense from a user-perspective and its functionality completely destroys the offerings from the competitors.
I could keep going, but I think those are enough

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wow....please DO go on....I think you just made me switch to Opera...(again)...the right click and scrow wheel thing is sooooo crazy...the first time I did it I was like...
wow...
Please..do go on...I must hear more of these very very intersting features...
Ok...now I'm deadly intersted...how do you do mouse gestures?...