Turner used CNN International as overnight filler when CNNfn was off air. When CNNfn shutdown Turner gave providers the option to carry CNN International 24/7, but most providers opted to drop it entirely.
I'd like to have CNN International back. I gather from this old thread that it was dropped in 2004. I'd like to watch Richard Quest's and Christiane Amanpour's shows, for instance. It is carried on some cable systems.
As for CNN International HD, the North American feed isn't available in HD yet.