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Cinema display or LED cinema display? If it's the old cinema display with DVI, just buy a DVI cable. Both, iMac and old cinema display have DVI
 
Dangit! :( Do the new iMacs allow for compatibility, or am I just stuck in general?
 
there is a dvi to minidisplay adapter....

I know, but I think it works only other way around. If your computer has MiniDisplayPort and your monitor has DVI then it works. What I've hears, the only way to hook something to new LED display, is via DisplayPort

For the OP, yes new iMacs have MiniDisplayPort, so you can hook 'em to LED display
 
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