Short Version: Tech Support at Monoprice has recommended using a minimum of 4' HDMI cables (as opposed to using, say, 2' or 3' cables), even as interconnects between components / receivers. The Reason given was that "it takes 4 ft for HDMI signal to reach maximum strength again." I couldn't find any individual corroboration of this, so I turned here.
Longer Version: I currently have a setup like this...
Components (PS3, etc.) -- <3' 24 AWG HDMI cables> -- Onkyo TX-SR608 AVR -- <50' 22 AWG HDMI cable> -- Mits HC6800 Projector
Video processing on the Onkyo is off, so it should be passthrough. I use the PS3 as my Blu Ray player, and even with the 50' cable directly connected from the receiver to the projector, I occasionally get handshake issues and signal dropouts when using the PS3 (movies in 1080p and sometimes even games in 720p.)
I was considering replacing the 50' cable with one of Monoprice's HDMI over Cat6 STP solutions, and was going to use 1' HDMI cables at each end when I got the advice from them about using a minimum of 4' HDMI cables, which I found surprising.
So, any and all input is welcomed. If you think the Cat6 solution is worth trying (or not) and have any experience with it, I'm interested. Of course, I'm also interested in the "minimum HDMI cable" question.