>> From teamxbox.com:

The first thing I did when I got my hands on the HD-DVD drive mock-up Microsoft had on display at E3 06, was to check its back side. When I found that there was only a power socket and three USB ports, I approached a Microsoft representative to ask where the HDMI port was, or if they plan to release an HDMI Xbox 360 AV cable when the external HD-DVD drive launches. His response was:
"If Sony is not using HDMI to play Blu-ray Disc movies, neither are we."
To which I immediately replied, "But the AACS spec demands the use of HDMI or DVI in order to playback HD content at its full resolution". Before I finished my words, he repeated,
"If Sony is not..."

I was a little surprised that a Microsoft representative would provide such an unsubstantial explanation for the lack of HDMI on the Xbox 360. Since when does Microsoft do things based on Sony's actions?
It is impossible that Microsoft would have decided to drop HDMI after learning Sony wouldn't include it on its base PS3 model, since Sony announced the world-shocking news a day before the Microsoft's Pre E3 briefing.... or did Microsoft already know, well before E3, that Sony was not implementing HDMI output on one of its PS3 models? It seems that indeed could be the truth.
A week after E3, a German newspaper spilled the beans on a supposed secret pact between Hollywood studios and consumer electronics manufacturers to disregard the implementation of AACS's "Image Constraint Token". This would mean that the lack of HDMI would not prevent HD-DVD and Blu-ray Disc hardware from playing high-definition content over analog connections at full resolution.

This pact between Hollywood and consumer electronic manufacturers might never be officially announced and all the parties involved will probably offer the classic "no comment" line. It's even possible that after establishing that secret pact at the AACS LA, Sony and Microsoft had their own HDMI-related agreements.
Since the pact between Hollywood studios and CE manufacturers is rumored to postpone the use of the Image Constraint Token until 2010 (possibly until 2012), neither the Xbox 360 nor the PlayStation 3 will need a HDMI connector since consoles' lifecycles are usually five years.