Antique Question Roadshow
Very out of date question, here is a modern answer:
At the time of the question, Chrome and Firefox did not have color management, while Safari and OS X has been color managed for a very long time. The web's standard is sRGB - but for that to work with a non color manage browser, the monitor must be calibrated (not just profiled) for compliance with sRGB.
Today
Today, Firefox and Chrome are color managed (depending on version, may only apply to images and not CSS colors).
To force a certain ICC profile in Chrome, you can pate this into the address bar:
chrome://flags/#force-color-profile
Nevertheless, many mobile browsers are still not color managed (color management uses a lot of processor resources).
The Wide Wide World of Gamuts
I am answering this old question because I want to address something else: If you are using a standard sRGB monitor, and your color managed browser does not match an sRGB image displayed in a non-color managed browser such as older Opera, then your MONITOR is way out of adjustment, or does not meet sRGB. If you are using a wider gamut monitor this is to be expected.
While there ae a few "wider gamut" monitors/displays such as Apple's Display P3, and AdobeRGB Wide Gamut monitors, most monitors on the market are intended to display sRGB.
To use a "wide gamut" monitor, you essentially MUST have color management, and use color managed apps for anything where color is important.
But if you are using an sRGB monitor, things should work without color management if you can adjust your monitor to match the sRGB specifications. This because sRGB is a display-referred colorspace that is also the standard for the World Wide Web. And while CSS4 will be adding additional colorspaces, sRGB will remain the default space for the foreseeable future (there are some accessibility reasons that sRGB is better suited for).
You can actually have better performance if you do NOT use color management, and instead ensure your display is properly calibrated to sRGB. If you can.
Calibration
If you are using color management, and you want accurate results, you really need a hardware calibrator/profiler and software, such as the XRite i1 Display Pro.