I believe most people use component cables when capturing from xbox/ps3 which gets round the HDCP problem and for SKY HD some of the old boxes had component, not sure about newer ones, but don't think they have the connection.
As for what capture card to use, I believe most youtubers use this Hauppauge box -
http://hauppauge.co.uk/site/products/data_hdpvr.htmlI myself bought a Black Magic Intensity last year to try recording vids from my 360 and while it does work over component, I had a few compatibility issues with my motherboard (Asus P5B-Deluxe). It seems the PCI-Express x1 slot on the mobo is a little too far in or the BM card is too short as it didn't reach the back of my case properly, causing the card to sometimes not be seen by Windows. This meant constantly reseating it, so I eventually pulled it out and it's now in a cupboard somewhere.