There are some HDMI splitters made specifically for this sort of application, but they can be quirky (HDCP doesn't like to play nice with such things).

Component video is unaffected by HDCP, since HDCP is a digital protocol for copy protection and component is an analog signal. Component video can handle 720p or 1080i, and as long as nobody starts turning on the ICT (image constraint token) Blu-ray discs can be output at those resolutions. You can't do 1080p, though, and you won't get higher than 480p with copy-protected DVD's. And eventually (around 2012), the BDA has said that new Blu-ray players will be required to start phasing out analog video output, but that doesn't yet need to enter into the equation.