If you use Internet Explorer, as most people unfortunately do, you are really not getting the most out of your time on the web.
These are just some of the things that Opera can do:
Not only can you bookmark individual pages, but you can define a set of pages and open all of them in one go - or have Opera load them all when you start up.
If Internet Explorer crashes, you have to remember which pages you were looking at and type the names in again. If Opera crashes (which it doesn't do very often), it remembers all the pages you were looking at, and will put you back exactly where you were (if you want it to).
Pop-up blocker - if pages have pop-up adverts that drive you mad, Opera can ignore them for you. No more adverts! But if you click on a link that opens a new pop-up window, that will still work, because you've asked it to open the page.
Pictures taking a long time to load? With IE, you can turn pictures off, but it involves going through lots of menus and takes ages. With Opera, just one click turns off all images. Another click allows images that you've already loaded and are 'cached' to be shown (but won't download any more unless you specifically tell it to), and one more click turns all images back on.
Several pages running at once? When each one has finished loading, Opera turns it blue in the taskbar at the bottom of the screen - you can see straight away that it is ready, but it doesn't come jumping to the front and interrupting you if you're busy on another page
Zoom in and out at the touch of a button if text or pictures are too small - or too big! From 20% zoom out right up to 10× magnification - just Control and scroll
Does someone's colour scheme hurt your eyes? Is the text way too small, or in a font that's hard to read? No problem! Opera allows you to turn off 'style sheets' with just one click, so you'll just see the plain text of the page without any formatting. No, you probably don't want to look at all websites like that, but some of the ones that are badly done - it's the only way you can read them at all.
This is a really great feature for web designers. You can check what your page will look like in all sorts of settings, such as high contrast or WAP devices, to get a feel for how other people might see your website if they are using a different setup to you
If you have two websites open at once, does it really bug you when one page keeps popping up in front of the other one? When windows resize themselves to fill the screen without you telling them to, does that get your goat? Opera allows you to turn this tiresome behaviour off, so you see the windows that you want to see, at the size you have chosen.
It's quick - it loads pages much quicker than IE, renders graphics, runs scripts, opens, closes - everything is so fast!
You can turn on and off Java, Javascript and plug-ins instantly if they are annoying you - no need to wade through loads of incomprehensible menus and dialog boxes
It's fully customisable - you can have it set up and laid out exactly as you want it
Just press 'Z' to go back a page and 'X' to go forwards again - great if you're holding your phone, cup of tea or whatever in your other hand. Get to your most recent page and press 'X' again, and Opera will look for a "next" page in the sequence to go to.
Extensive support for CSS2 makes it one of the most advanced and capable browsers around. The few features I've used on this site barely scratch the surface of what can be done. More and more web designers are starting to use these tricks, but IE doesn't support any of them properly
It's secure, and it does what it's told. If IE comes across a badly-written website (and by that I mean that it has been poorly coded, not that the grammar and punctuation are sub-standard), it will guess what it is supposed to do, which can lead to a horrible mess. Opera displays the page exactly as it has been told to do. And because of this, it is much more secure - viruses for IE are as common as muck, but viruses that attack Opera are as rare as rocking-horse poo.
Faster searching. If you just type a load of words into the address bar of IE, it will do some sort of a general search for them, but that might not be what you want. In Opera, there are 18 different search engines that it can access automatically - just type "g car insurance" and it will search Google, type "z harry potter" and it will search Amazon, with different key letters you can instantly find domain names, get Ebay listings, do a price comparison and all sorts of other weird and wonderful things
See a word and don't know what it means? Double-click on it and you can look it up in a dictionary, encyclopedia, or translate it into another language (or from another language into your own - might be more useful) at the touch of a button
That's all I can think of for the moment - apart from that it's free and you can download it in just 3MB - that's about a quarter of a full installation of IE6