The first had the registry number NCC-1703 and was featured in the original Star Trek episode, The Ultimate Computer. In 2268, it was destroyed by the U.S.S. Enterprise during the test of the M-5 computer system that caused the Enterprise to fire on four other Federation ships.

The second U.S.S. Hood's registry number was NCC-42296. It encountered the U.S.S. Enterprise-D a number of times. First, it dropped Commander Riker off at Deneb IV after his tour of duty their ended and carried Admiral Leonard H. McCoy so he could do a pre-departure medical inspection of the Enterprise. On stardate 43463.7, the Hood and the U.S.S. Monitor were diverted to the Nelvana area in response to reports of a Romulan base there by defecting Romulan Admiral Jarok. Around stardate 43741, the Enterprise was going to rendezvous with the Hood for a terraforming project until Captain Picard was kidnapped and the meeting was delayed. Under Captain DeSoto's command, it met up with the Enterprise to drop off Tam Elbrun for the " Tin Man" mission and was among Picard's blockade fleet on the Klingon-Romulan border during a Klingon Civil War.

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Sources:
http://www.startrek.com