The cable guy's coming tomorrow to install an HD Digital box at our house. It has a DVI out, so I'm definitely connecting that to the 970's DVI2 input, for the sake of the HD front projector. I also have a smaller CRT hooked to the 970's analog monitor outputs, however, for times when I don't want to pull down the screen and turn out the lights.

My question is, do I need to use both analog and digital video connections from the cable box, in order to get an analog video signal for my CRT, or does the 970 create an analog signal from the DVI input?

The 970's DVI switching is purely switching, so the DVI input will not be passed to the analog monitor outputs. You would need to connect both - but make sure that the analog connection you use is active at the same time that DVI is (my HD cable box disables the component video output when DVI is active, although composite and s-video both remain active).