Even though Opera is the most popular mobile browser in the world, in the desktop market Opera is the most under-rated browser despite having created many innovative features. Which were later copied by other browsers.
Its hard to understand why Opera has only ~2.2% browser market share while IE6 still boasts a whopping ~14.5% market share. Maybe the Opera developers were so busy developing solid browser features that they forgot that they need to do some promotions in order for people to use it. In contrast IE developers were so busy shoving their crap browser down peoples throat they forgot to make a half decent browser. Whatever is the case, the internet is a better place today thanks to some of the innovations that started from the Opera camp.
Source (with a grain of salt)
1) Speed Dial: First introduced by opera in 2007, copied by Chrome since the beginning, added to Safari 4 since beta and can be added to Firefox in the form of an extension.
2) Tabbed Browsing: There are some disagreements about who introduced tabbed browsing. The first version of Opera in 1994 (named MultiTorg Opera) introduced MDI tab where each tabs could be resized, tiled, cascaded and moved. But Netcaptor in 1997 was the first browser that offered the current form of simple fixed tabs that we are used in browsers (but at the bottom). Tabs on top of the browser (unlike Netcaptor) was also introduced by Opera in 2000.
[ Tabs in general applications was first introduced by IBM and adobe holds some sort of patent for tab functions, but thats a different story ]
3) Sessions: The ability to save browser session was introduced with Opera 2 in 1996. If you close your opera browser or it crashed you can go back to your last auto saved session including history of that session. This feature has been since copied in one form or another by other browser but none of them are as extensive as Opera session, where you can save a whole session of browser history in to text file and transfer in to a different computer and resume from there.
4) Pop-up Blocking: Imagine a web experience without pop-up blocker. What we take for granted today was first introduced by Opera 5 in 2000. Firefox picked it up soon and IE joined in the party in 2004.
5) Full page Zoom: A better alternative to larger text, zooming increases the size of the page without distorting the layout by only increasing the text size. Introduced by opera in 1996, and now all major browsers have this feature.
6) BitTorrent: Opera was the first to have torrent support built-in to the browser since 2006. It uses its download manager to download a torrent file like a regular download.
7) Delete Private Data: The ability to remove personal information from your browser was first introduced by Opera in 2000. We had to manually delete personal info BO (before Opera).
8) Mouse gestures: Using mouse gestures to perform repetitive tasks like scrolling tabs, closing tabs, back and forward button using gestures was meant as an alternative to keyboard shortcuts for maximum productivity. This feature was introduced by opera in 2001 and now Firefox supports this functions with the help of an extension.
Conclusion: This is not a complete list and Opera was not the only browser that had unique ideas and innovations that changed the way people use browser. But no other browsers had so many innovative ideas that has been copied with great success by almost every other browsers. Yet, Operas market share is still around 2% while other browsers are benefitting from its ideas.
The Opera team will have to take some blame for not doing enough to promote their browser in desktop market (they are big in mobile browser market), also for the longest time Opera has this stigma attached to it because it used to be a commercial trialware browser and later ad-sponsored. But since 2000 they moved away from trialware and from 2005 they removed ad-sponsorship. Will they ever be a major player in the browser market share, now that the competition is greater than ever? Difficult to predict, but hopefully we will continue to benefit from great ideas delivered by the Opera team.