As is already being reported, Ubuntu will shortly release Ubuntu 6.10 ("Edgy Eft") and it will include Mozilla Firefox 2.
Matt Zimmerman from Ubuntu has announced this on the ubuntu-devel mailing list, and anyone following their release process will have noticed this already too. As you may know, Mozilla's relationship with the Debian project has been an issue lately, and I'm sure that this announcement raises some more questions given that Ubuntu is based upon Debian.
We've put together the following Q&A. Please do let me know should you have any other questions.
Will Ubuntu be shipping Firefox?
Yes. Ubuntu 6.10 will include Firefox 2, just released this week by Mozilla. 
Is it a full and official Mozilla Firefox release?
Yes. Ubuntu will be shipping an official and supported version of Firefox to be fully branded as "Mozilla Firefox 2".
Is this the first Linux distribution to ship Mozilla Firefox?
Ubuntu will be the first Linux distribution to ship with Firefox 2. Red Hat, Novell and other distros have been working with Mozilla and currently ship an official and supported version of Firefox 1.5. We expect that they will update to Firefox 2 in due course.
I understand that Ubuntu is based upon Debian. Is that the same or different than the IceWeasel browser that Debian is shipping with their latest release?
It's different. The patches that Debian applied to the Mozilla source code (which then resulted in their IceWeasel product) are more significant in scope than those in what Ubuntu is shipping (and branding as an official Mozilla Firefox release). Firefox in Ubuntu represents a somewhat more modest set of divergences from original Mozilla source code.
What's different in the shipping Ubuntu version of Firefox than the proposed Debian version of Firefox (that didn't ultimately ship)?
Technically, changes include fixes to the User Agent string and the feed preview, a well as addressing issues of coherent branding. More significant than any specific difference in code, however, is Ubuntu's commitment to work together with Mozilla and our community on releases going forward to insure product quality and integrity.
Why are you working with Ubuntu when you wouldn't work with Debian?
We did try to work with Debian and would prefer a situation in which we work together. Ultimately, Debian took a position that was consistent with their own policies, and not compatible with some of the exceptions to Mozilla trademark policies that we offered. While we understand and respect their decision not to work with us under our branding guidelines, Mozilla believes that brands like Firefox are important for consumer protection. In any event, Ubuntu developers are working closely with Mozilla developers to insure product quality and features that are what users expect when they use Mozilla Firefox, which means that they'll ship (and will continue to ship) a fully branded version.
Should we expect different versions of browsers in Ubuntu and Debian in the future?
We don't know. This is within the purview of both Ubuntu and Debian. We have every intention of working with Ubuntu for the foreseeable future to deliver Mozilla Firefox in same manner as we do with other Linux distros such as Red Hat and Novell.
Does the same logic apply to Thunderbird and IceDove?
Yes.