Yes and no. Yes, some really expensive rigs like the lightbridge from DJI can beam HD. These FPV quads typically have 2 cameras on them. The one on top in the pic above is a HD Mobius camera (Ebay). There's a second camera beneath it inside the frame (A sony security camera). They beam ~640x480ish video over 5.8Ghz to either a monitor, or goggles like these:
http://www.modellhobby.de/k_staufenb...SV3300_b_2.JPG
If you're using 5.8Ghz to beam video at > 25mw you'll need your technicians license (as mentioned previously).
The quality of the FPV feed is not usually great, but the range can be pretty awesome (think kilometers).
https://www.youtube.com/watch?v=dJ9URBcYOOk