I know that you can have the Mac's screen appear on a TV using an HDMI to DVI/Mini-DVI connection to the mac, but is there a way to make the reverse occur using the same connection (The Television's video to appear on the Mac)?
There are a handful of very expensive capture cards with HDMI inputs, but even if you had one most HDMI signals (from a blu-ray player, for example) have HDCP copy protection so wouldn't be recordable anyway.
If you just want to record low-to-medium quality video off a TV tuner, though, you can get an inexpensive video capture device and plug it into your VCR/cable box (it would have "composite", "s-video" or maybe "component" input). Alternately, get a tuner for your Mac such as the ones Elgato makes: