Buy the house next door and stash the TV there.
Seriously: Genevieve Gorder often says "everyone has them," by which she means that the TV doesn't have to be given a place of honor or be the sole focal point.
On the other hand, since (almost) everyone has a TV, it doesn't have to be treated as something to be ashamed of. I could argue that, if you intend to watch TV at all in a particular room, there's no reason to hide it.
One option that works fairly well with a flat screen, if the casing is dark, is just to recess it slightly in a wall of shelves, and display more interesting things on either side (perhaps lighted). When it's off, it's hardly noticeable.
Other than those two ideas (put it somewhere else, although usually that just means another room, and let it slip into the background when it's off), there is not much to do other than (1) put it inside something or (2) put something in front of it.
Candace Olson has done a number of different things on her show. One very nice effect put display shelving on either side of the TV, each section half as wide as the TV, with sliding panels that revealed either the TV in the center or the display shelves at the ends. That is, either the TV or the shelves would be visible at any given time; it wasn't possible to hide both, or to show both, simultaneously. This was all custom-built, not purchased.
She has also used a painting on a motorized panel, and a device that lifts an LCD TV out of a cabinet. I don't know where you would obtain either of these.
Q
Layered rug
Q