I want to be able to connect all the TVs in my house to my cable, satellite or Internet hub wirelessly. I would like each TV to be able to switch to any channel independently. Is this possible, or just wishful thinking?
At this point I would say wishful thinking with a theoretical application. It is possible but it would require a lot of preparation, setup and quite some investments into hardware.
For example at this moment there is no way to transfer a satellite (DVB-S) or cable (DVB-C) wireless. So basically you do have to put a wire connected receiver at some place. Then you would have to invest into a Wireless Transmission Kit (sometimes called WiCast) to get this signal from the receiver to the television.
Since you want to connect all TVs interdependently the above setup is necessary for each TV. If you have 3 of them you need 3 receivers and 3 Wireless Transmission kits. Another unfortunate point is that most receivers are either satellite or cable and most WiCast devices only have a single input.
For 3 televisions connected to both, satellite and cable, you are most likely looking at 6 receivers and 6 WiCast kits.
The only other setup would be a server PC with multiple DVB-S & DVB-C cards that transmit the signals wireless and something like an Eee PC at each television to receive the signal with the video out connected to the TV.
All if this is merely theoretical because you probably want to switch channels once in a while so you do need some remote/control connected to either the server PC or the receivers.
Possible, yes ~ practical application, a horror.