I can remember Opera having a "critical" security hole some time ago. I guess the hackers have been drawn away from it lately because of Firefox though.
As for "non-IE", "non-Gecko", "non-Conformist" standalone browsers they are pretty scarce. Here's one for you:
Off-By-One Browser.
"The Off By One Web Browser may be the world's smallest and fastest web browser with full HTML 3.2 support. It is a completely self-contained, stand-alone 1.2 MB application with no dependencies on any other browser or browser component. For Windows 95, Windows 98, Windows ME, Windows NT, Windows 2000 and Windows XP.
Now, with a tabbed browsing interface."
Off By One Browser Features
* Implements full HTML 3.2 support plus many HTML 4.0 extensions, including Frames.
* Secure Sockets Layer (SSL) support provided by optional OpenSSL libraries for secure navigation to https:// addresses.
* Incorporates a tabbed browsing interface.
* Extras include image animation, WAV and AVI playback and the ability to automatically launch external applications for file types that are not supported internally.
* Packaged in one self-contained 1.2 MB application. Can be compressed down to about 460KB for distribution.
* Completely self-contained, does not require the presence of any other browser.
* Does not require any installation, browser can be run directly from a CD or over a network.
* Has a unique Find-In-Files feature that can search the non-tag text of multiple HTML files.
* Has a unique image zoom option.
Off By One Browser Limitations
* No JavaScript support (so no pop-up ad windows).
* No applet, plug-in or Flash support.
Also it doesn't use a disk cache instead it renders webpages into memory, so when you close it there's no messy leftovers.