You cannot capture HD in HD.....yet anyway. You can only capture it to standard def, or 480 analog.
There is copy-protection built into the digital stream itself, which is why you need a HDCP compliant video AND monitor to view full res Bluray and HD-DVD on a PC (without the video dropping down to SD).
EDIT: Digital tuner capture cards are for HD over-the-air antennas, not for satellite and digital cable. If you hook your box to it, it will capture using analog input.
If the poster really means HDTV he or she is talking about 720p or 1080i material. This can not be captured using VIVO cards with just S-Video or composite inputs (480i).
Furthermore, if you are using a VIVO connector for input, you can not use the 1080i output of the card.
Well-intended but not quite accurate. Yes, the OP is writing about HDTV, not BluRay or HD-DVD, and use of his/her set top box. Further, I didn't suggest s-video, I wrote "composite" input, but other possible inputs could also include component, or HDMI.
Use of the fustion card, the same one I recommended (QTF),
initiallyTake a look at these; not sure if they have the inputs you need, but check it out:
http://www.fusionhdtv.co.kr/eng/Products/fusion5express.aspx
does not preclude HD capture, however, it just means that you can't get rid of the cable box -- if you can capture OTA HD, you can capture HD from the cable box output as long as your output matches the TV tuner input, you just can't use scheduled programming through something like MCE, as you're still bound by the set top channel changer, as paulpod pointed out. (Other posters should read the inital posts and links before giving duplicate or inaccurate info, esp, say, the one on HD capture from HIS). This is distinct from HDCP content as encoded on BluRay or HD-DVD, and has nothing to do with TV broadcasts, (yet). This from the Fusion Website:
With this product not only will you receive analog and terrestrial HDTV broadcasting, but also cable HDTV receptions
You will still need a video card capable of displaying the HD content on your TV, by whatever output: DVI, HDMI, etc. Frankly, I've got a receiver that will take a 480 s-video feed and upgrade the signal to 720p (or 1080p) and output it through HDMI to the TV, no HDCP needed. As paulpod suggested, an ATI-based card with the built-in Theater chip is excellent for this, and if chosen wisely, will more than likely have HDCP-ready capabilities anyway. I would suggest something along the lines of the X1950Pro cards. In any event, here's a list of HDCP ready video cards:
http://www.hardforum.com/showthread.php?t=1071342