In my home theater I have the following source equipment:
Blu-ray player (it was purchased before the PS3, and I keep it in my system because it integrates better with my Harmony remote)
Unfortunately, my receiver (Onkyo TX-SR705) has only 3 HDMI inputs and my Mitsubishi 1080p projector only has one. It does have a DVI input, however.
In order to get the highest quality signal on every source, my connection preference would be: Xbox, PS3 and Blu-ray to the receiver via HDMI, and TiVo to the DVI input plus optical digital audio to the receiver; however, I have been unable to get the TiVo to sync to the DVI input with a standard HDMI->DVI cable. So currently I have the TiVo connected to the receiver via component video, which then upconverts it to 1080p and sends it to the projector. This is less than ideal because the digital signal is being converted to analog and then back to digital.
The reason I don't want to use the DVI input for one of the other sources is that I will lose the potential TrueHD sound from these sources; however, I'm not sure that it will make a difference for the PS3 or the Xbox (that is, using audio over HDMI vs. a separate optical audio connection).