HD video requires a lot of bandwidth and processing power to get it down from the aircraft and displayed with a latency that is still usable to fly by. I haven't yet seen solutions for this but people are working on it...
Some professional solutions for streaming full HD wirelessly exist, but I doubt you are looking to spend thousands just for that. Also having some latency isn't an issue when the purpose is to just get the footage, not to fly by the feed. The hobbyists will get there too though, eventually...
How about the Gopro. I have been reading it can record and stream at the same time. I assume its a reduced resolution that is streamed?
While it records, it can output standard definition video, with some delay. I do not know what amount of delay it has, but I hear it's not fatally high for calm flying. Still, it has some delay and it's not even HD.
I have been working on a solution that will do this. It is pretty expensive. I have a MicroHard VIP5800 radio that is essentially an ethernet bridge with a high speed serial sideband. I am taking HDMI video output, doing H264 compression and then sending it via the radio down to a ground station. The radios are about $800 for each end, but I picked them BOTH up from a guy for $350 along with some wiring and supporting hardware. Once I get it up and running I will post results, I am still waiting on some of the hardware. I'm curious why one might want to stream the HD video? I am only doing it because on my camera when you connect the control cable you lose the composite output, and only have HDMI to work with (Bad Sony...Bad!)
I would be interested in it "just because". ;-) Other reasons might include live coverage - imagine being able to stream good quality live video to a big video screen in some event!
I wonder how much it would cost to make a minimalistic PCB with some suitable system-on-a-chip capable of h264 encoding in hardware and pushing it out a PCIe lane to a wireless networking adapter, with maybe some telemetry on the side via a serial port or two. If the Raspberry Pi can be made with a couple dozen bucks, surely something like this could be done affordably too - if you just got together a group of people interested in designing and preordering it in a sufficient volume.
You know what also might be interesting, is the use of a Sony HDR-TD10 3D camera and the Sony HMZT1 Head Mounted 3D display, but I am sure that would all just compound the transmission issues.