The first Enterprise was destroyed in The Search for Spock, the build another one. In the Next Generation they are in some new looking "Galaxy Class" Enterprise. Were there any other Enterprises in any of the Star Trek series?
Was ist der Sinn des Lebens?
Going by canon, and counting the NX-01, 12. You have the series starting with NCC-1701, and "Enterprise" had the NCC-1701-J, but the only ones seen are the original, A-E, and as mentioned J.
shareWell, 7-8 for what was seen officially on screen; NX-01, NCC-1701, NCC-1701-A, NCC-1701-B, NCC-1701-C, NCC-1701-D, NCC-1701-E and the purported J. There would invariably be F-I off screen and over the course of the years between E being decommissioned and when Daniels was alive, but J seems barely worth counting, being a random, brief appearance; adding all of the other generations of Enterprises solely on that one reference seems like a cheat.
While for all intents and purposes of what they presented, Daniels' story and all of his claims are cannon as being true; personally my own personal fan theory is that a fair amount of his claims were more often than not lies, to try manipulate Archer. It just seems dubious for a professional time traveler to be as reckless as Daniels ended up being; being so loose with future knowledge and direct interference.
If I had my druthers, and I realize I don't, I would retcon Daniels' whole story to reveal that his claim of being from the 31st century is totally bogus; he's from the 24th century and an operative of Section 31. In fact, basically any other human claiming to have been from the future, like Captain Braxton on Voyager, who weren't otherwise debunked, were all really Section 31 agents in the 24th century; still using time travel technology, mind you, but trying to cover their tracks. Daniels thought he was being cute embellishing his cover story by making his century the "31st". The battle he showed him with the Enterprise J was all a lie. It all largely stems from the fact that it's hard enough for those shows to create realistic conflicts where the outcome isn't predictable, but those stories pretty much say outright that the Federation will exist and prosper for centuries to come, and humanity basically becomes time lords in the next millennia. Which is possible, but to spell it out like that takes away what little suspense they're still able to maintain, when you can reasonable be certain already that the main characters are going to survive every major threat from week to week.
“Well, that's called tyranny; and its generally frowned upon."