The Canonical ship of the Star Trek Franchise. There have been a number of Enterprises over the years. This is not intended to be a complete history of the ships, that is well done elsewhere.
In Canon[]
NCC-1701[]
Constitution class and Constitution Refit. The original, the ship that told us that space ships didn't have to be saucers or missiles.
The Enterprise no bloody A, B, C, or D is first seen in three seasons of Star Trek TOS and last seen in Star Trek: The Search for Spock were it is destroyed. In Star Trek: the Motion Picture we see the refit Enterprise. A model made for the Star Trek Phase II series that was canceled in favor of the Movie. To the author's thinking the fairest of them all.
Captains:
Robert April
Christopher Pike
James T. Kirk
Will Decker
James T. Kirk
Spock
James T. Kirk
NCC-1701-A[]
Enterprise class. Obviously without the Enterprise we don't have a franchise. So the ship destroyed in The Search for Spock is resurrected as the 1701-A in The Voyage Home. We get to enjoy her right up through The Undiscovered Country.
Captains:
James T. Kirk -- That we know of.
NCC-1701-B[]
Excelsior class variant. The "B" was seen briefly in the fist part of Star Trek: Generations. The Modifications to the secondary hull were done so that damage to the Excelsior model would be of a temporary nature.
Captains:
John Harriman
Pavel Checkov -- No it's not Canon, but there is a very nice set of fan fiction called Checkov's Enterprise, and I like it.
NCC-1701-C[]
Ambassador class. This ship was briefly seen in "Yesterday's Enterprise", an Episode of Star Trek TNG. We never really get to see anything of her. The model makers did a nice job of a middle ground between the Galaxy class and the earlier designs.
Captains:
Rachel Garrett -- again, that we know of.
Richard Castillo
NCC-1701-D[]
Galaxy class. The main ride for the entire run of Star Trek TNG and Generations where she was destroyed to keep Andrew Probert from making any more money off it. Really, it was the only reason for the whole end of the film.
Captains:
Jean Luc Picard
Epiphany Trek[]
The Enterprise D is not destroyed. She received the DiSodium refit and is now one the dowager queens of the fleet.
Captains:
- Jean Luc Picard
- William Riker
NCC-1701-E[]
Soveriegn class. The ride from First Contact to Nemesis. A pretty mover. Also the first time a new Enterprise was smaller than the last one. While longer, the ship is a fraction of the mass of the Galaxy.
Captains:
Jean Luc Picard