The only practitioner of the read-write web, Konqueror soldiers on
For a long time, Konqueror was just about the best thing in KDE. Not only was it a capable, standards-compliant browser (although at the time nobody had worked out how to support all those proprietary extensions), but it was also an awesome file manager.
The two functions sat side by side, and the implementation of KParts means that, in Konqueror, pretty much everything is just an object to be rendered and interacted with, whether it's a local directory, a remote FTP site, a Samba share, a website or whatever.
Times change and, although old Konqy is still the default browser for KDE, its filesharing function has been hijacked by Dolphin. Its rendering engine is another story – that was used by Apple to produce the WebKit library, powering Safari and a great number of other browsers.
Konqueror is just about the only browser still sticking to the KHTML renderer, but why not? It may not be the fastest tool in the box anymore, but it still does a reasonable job of supporting standards and supports a great amount of HTML 5 already.
Raw speed in downloading and rendering pages is one thing, the speed at doing the things you want to do is another. Konqueror's KIO and ability to run as a file manager make it much more efficient if you're uploading files to FTP sites or WebDav shares, because the interaction is seamless.
Most browsers are designed as consumers of the web, but Konqueror treats the web as just another resource to be read from or copied to.
Konqueror also has a pretty low footprint on the KDE desktop, because so many of the resources it needs are already loaded, in comparison to the likes of Firefox or Chrome.
Slightly left behind in the speed stakes, but still a versatile tool
Opera stands out with an unusual take on what a browser should be
Opera Turbo is a nifty compression technology that could boost the speed of many websites, for example (though it's impossible to really empirically test this, it does seem to work for some sites).
Opera Unite is another interesting feature, which builds a kind of personal network between the user and friends (who also use Opera) to share files, links and other information. In short, there's plenty of thinking about the user experience going on here.
This is a very able browser with all the security, personalisation and privacy features you would expect. For plugins, it relies on loading your Netscape-style libraries, and features widgets rather than extensions. The difference? Widgets are less like alterations to the browser, and more like specific tools or clients for web services, such as the weather.
The 10.50 release for Linux has been a long time coming, but you can download a beta version for testing now.
Great web experience, though the speed claims are unfounded.