My (probably inaccurate) knowledge tells me they cannot do the same to analogue monitors like the good old CRT monitor that I've used so far. Is that true?
No its not true.
All signals coming from your PC start off and are processed as digital signals, CRT monitors do not accept this signal as usable so the video card of your PC needs to convert it to an analogue signal it can process, mostly RGB. That's carried by the VGA connector (normal 15 pin D Type) to your monitor.
LCD displays are digital, so if you use the VGA connector the display has to convert this RGB signal back into a digital signal it can use.
Thats where DVI cables come in, they carry he raw digital signal to your LCD monitor. If your PC can output a digital signal and your monitor can read a digital signal why convert it to RGB and then back again.
Microsoft's vista will screw with the digital signal, so it will not be viewable on either LCD or CRT equipment.