Good news! Mozilla added color-management to Firefox 3.0a7. I instantly downloaded this version and tried it with my Win32 laptop: Hey, it works! There's a test on the ICC website ( http://www.color.org/version4html.xalter ) and Firefox passed it.
I was looking a little into the code changes and they are using LittleCMS for color-correction. So how can it be enabled?
Open about:config in Firefox 3.0a7 and set gfx.color_management.enabled to true.
Then either the monitor profile set in gfx.color_management.display_profile is used or then as a fallback the one provided by the system (already implemented?) and if even then no profile was found the sRGB profile integrated into LCMS is used.
There's a bug asscoiated with this new feature: https://bugzilla.mozilla.org/show_bug.cgi?id=16769 . There a lot of information can be found of what is working and what not - I will read it completely later ;-)
One of the problems seems to be that plugins (Flash!) are currently not aware of it and so it may be hard to get the same color in HTML and Flash.