There are at least 2 questions you need to answer: do you need/have HDCP and can you live with the aspect ratio of the monitor, which is more likely 16:10 (e.g. 1920x1200) rather than 16:9 (1920x1080).
My comcast box has DVI out up to 1080i, but HDCP is required.
The dell 24" LCD has it, but maxes out at 720p using HDCP with current versions. Such a shame considering the native is 1920x1200, otherwise it would be an ideal hybrid monitor for work and play.
Otherwise you usually need a HDTV LCD or a
"HD-Ready Monitor" LCD (or whatever way they call it now) which is one without a tuner but has HDCP.
Nearly dead silent HTPC ver 2.0: i3-4340 w/ Noctua NH-L9i on Z87E-itx inside CM130 elite, fanless PSU, SSD OS drive SAN shares via 40GbE tunneled over 56Gb infiniband links microcenter & ebay = severe risks to my wallet