Your Mac mini
cranks out its video via DisplayPort and audio via a mini Toslink. Chances are your home entertainment system doesn't like either of those. It will, however, like the Kanex Mini DisplayPort Adapter, which can turn a DisplayPort video signal into a 1080p signal over HDMI, and will even integrate either digital or analog audio into the mix. It's USB powered, so there's no need for a clunky power adapter, and while $70 isn't particularly cheap for a chubby cable ($50 for the USB analog audio model), it's about the cleanest way to get your Mini pumping tunes and vids through your system.
[Via The Unofficial Apple Weblog