I'm a long time Opera user, I use Opera and Firefox depending on need but far prefer Opera for several key features:
1) Firefox 3.5 has some weird display issues with high dynamic range images (exhibits clipping in highlights and shadows) which is related to it's colour management. This has been seen in XP, Vista and Win 7 on multiple systems with calibrated and non-calibrated screens.
2) Firefox consumes more RAM, when it's got almost the same comparable functionality as Opera though extensions. With the same pages/usage patterns, plus Opera releases memory more readily.
3) Opera Link is a great way to share your bookmarks, notes, history, etc between my mobile/desktop computers.
4) Unite gives me control over my own content so I can decide who I want to share it with.
5) Opera is faster at both loading web pages and starting up.
6) In Linux Flash is far more stable with Opera than any other browser. The pain with some distros is that Opera IPv6 support is flaky.
7) Functionality is far greater out of the box with Opera, but they doesn't really advertise it's there so most people don't realise what's under the hood.
8) Tabs, Opera still has the best tab system of all the browsers. Thumbnails, locked tabs, drag and create new window and so on.
9) Shortcuts. Got several ways to open multiple pages either by assigning a word/letters to the bookmark folder or by creating a session. This way you can open 20-30 pages in seconds.
Before you think I'm a Opera fanboy some things that really need to be dealt with:
1) lack of meaningful widgets. Yes Opera is extensible but how easy is it? Also it's not advertised as broadly as Firefox. They way Widgets is also going to be different in 10.20 as they are going to be semi-independent applications in that they will run without Opera running but Opera still needs to be installed.
2) Dragonfly is a great start but we have to wait till the next Presto engine to get the new features? That's a long time between development cycles to improve functionality.
3) Better support for existing features, Opera has a nasty habit of adding features and then leaving them to languish.
In many ways Opera is for power users and researchers who spend some time learning it's quirks and features. Opera could spend a lot more time making it far more accessible to everyone, but like the additions of features Opera has a hands off approach which to be honest has hurt them.
Another factor is that Opera has never spent big bucks on advertising their browser, but yet pretty much dominates the mobile device market and is featured on some consoles.
It's not the perfect browser but in many ways it's far more refined and in comparison to Firefox 3.5 far more secure out of the box. Since 3.5 came out it's had 5 updates for both stability and security, Opera has had two; one was a security release and the second was a feature/bug fix. A lot of people feel that 3.5 was rushed out of the door and the subsequent releases back this up.