Below is a listing of the Constitution class starships seen or mentioned in Star Trek 
the original series and their registry numbers(some are canonical, some are best guess). 
These starships were first commissioned in the year 2245.


USS Constellation: NCC-1017 (seen in "The Doomsday Machine")
USS Defiant: NCC-1764 (seen in "The Tholian Web")
USS Enterprise: NCC-1701
USS Excalibur: NCC-1664 (seen in "The Ultimate Computer")
USS Exeter: NCC-1672 (seen in "The Omega Glory")
USS Farragut: NCC-1647 (mentioned in "Obsession")
USS Intrepid: NCC-1631 (mentioned in "Court Martial" and "The Immunity Syndrome")
USS Hood: NCC-1703 (seen in "The Ultimate Computer")
USS Lexington: NCC-1709 (seen in "The Ultimate Computer")
USS Potemkin: NCC-1657 (seen in "The Ultimate Computer")
USS Republic: NCC-1371 (mentioned in "Court Martial")
USS Yorktown: NCC-1717 (mentioned in "Obsession")