There are lots of ways to get Linux onto your TV. Node shows off how to build your own Linux-powered dongle that you can take with you anywhere.
The dongle is powered by an ODROID-W, a USB hub and Raspbian. You'll need some soldering skills to get everything hooked up, but once you're all done, you can connect it to any TV with an HDMI port, no extra cables required. It's not pretty, but since it's hidden behind the TV, it shouldn't really matter.