Can H.D. images (720p, 1080p) be recoderded on tape?

Professional tape, yes. Professional tape has gone through a couple of generations, getting more reliable and smaller. The first was the Sony HDD1000, which recorded on 1-inch tape with a helical drum using multiple parallel heads to get the full digital baseband recorded (over 1 Gbps). The unit was 19 inch rack width and about 20 inches (?) tall. The heads wore constantly and were sensitive to smoke and dust in the environment like you wouldn't believe. Later formats are much more reliable, the recorders are more compact, etc. Most production houses have worked their way through the tape generations and are now going to disk drives and other digital storage.

For home, there was some contemplation of a tape machine that could record the 19 Mbps compressed digital signal off the air. Nowadays, the only home recording is on Tivo-type personal video recorders, which record the compressed signal to a hard drive. Baseband HD tape recorders are not manufactured due to 1) cost (but that could come down quickly); 2) preference for hard drive or other systems, which can be cost reduced even faster; 3) paranoia of the movie studios about high quality recording and sharing of HD material, which paradoxically, is more likely a problem when recording to a hard-drive system with digital in/out. Maybe eventually home Blu-ray recorders will fill this niche, but it will be only a niche because of the copy controls that now exist, as compared to the ease of copying SD video to VHS tape.

Up until a few years ago JVC and Mitsubishi sold D-VHS decks but no more.

http://www.amazon.com/JVC-HM-DH30000L-Digital-Recorder-Silver/dp/B00005RI9I


http://reviews.cnet.com/vcrs/mitsubishi-hs-hd2000u-digital/1707-6476_7-31767258.html

There was W-VHS prior to D-VHS but it could only record interlaced video.
http://en.wikipedia.org/wiki/W-VHS