Can I connect my console to my apple cinema display?

No.

XBOX 360 and PS3 both supply a HDMI signal.

Apple’s cinema displays only accept a digital DVI signal.

There is no way to convert the HDMI signal from xbox into a DVI signal.

One company (forget which one) sold a special HDMI-to-DVI converter box for a bit, but they’re no longer selling it and aren’t intending to start selling something like it again.

If you’re buying a LCD computer display, buy one that has a HDMI input, or at least composite or VGA.

(figured I’d put this out here since it’s the 2nd time someone asked me, and I remember being really frustrated when I couldn’t get it to work)