Overlaying a video image on top of another, which in the production world is called "keying", is actually rather complex. The three main techniques are chromakey, which determines which image wins based on color (thus green-screen techniques, etc.), lumakey, which determines the winner based on pixel brightness, and alphakey or linear keying which has a separate signal giving the opacity of each pixel in the key.
There are quite a few keyers out there, but they are all aimed at the production market and are thus very expensive (e.g. multiple thousands of $$) and for HD signals they all pretty much use HD-SDI and not HDMI. I found a few video mixers that take DVI inputs, but the most I could find was 2 DVI in on a mixer that was a few thousand $.
If you're doing stuff in standard def and want to switch to composite or S-Video, then you can do it cheap. You might be able to make it work with component, but I didn't see any HD-ready analog video mixers. If you want to stick to HDMI, you're out of luck. Even if you wanted to try going the HD-SDI route, HD-SDI does not do HDCP, so most likely you'd still be stuck.