Five; Columbia, Challenger, Atlantis, Discovery, Endeavour.
The thing you need to realize about Star Trek (especially true of The Next Generation but could plausibly be applied to every other program that followed it) is that the USS Enterprise doesn’t have a crew because it needs people to tell it where to go and what to do; it exists expressly to give a purpose to people who have too little patience or intellect to stay at home and innovate, or people who are too anxious to sit in front of their holoscreens or whatever and subsume themselves in whatever entertainments the machine overlords give them.
Consider: it is clear that the crew of the Enterprise–even the featured experts that make up the senior crew–really have little understanding of what is going on with the ship or the phenomena they encounter. Sure, they go on “away missions”, make a show of tapping on panels and looking at streaming graphics, and “brief” the captain with loads of technobabble, but whenever they have a really hard problem to analyze, what do they do? They start asking the ship’s computer (and whatever ship they are on, it is the same voice with the same apparent capabilities) vague, often poorly structured questions, and somehow the computer miraculously interprets their requests and gives useful answer. Or, they go to the holodeck and create a “program” consisting of open ended descriptions and commands that allow the computer to produce a high fidelity simulation that answers all of their questions.
For some reason, the bridge has a full complement of officers crewing the “helm”, “sensors”, “navigation”, “weapons”, et cetera even though whenever they aren’t available the computer seems to respond to orders to use sensors or weapons just fine, and whenever the navigator is commanded to, say, “plot a course for Rigel Six” it is the matter of about ten seconds and six finger motions to perform what should be a complex feat of celestial navigation, tensor mathematics, and energy budgets.
But what about the aliens? Klingons, Romulans, Cardassis, whatever? They’re a real threat, right? They can’t just be in on the gag, too. And yet, no one on the crew finds it peculiar that virtually all alien life is not only humanoid in form but is actually sufficiently similar that expressions and body language can be interpreted without any “uncanny valley” effects? The aliens are clearly just synthetic organisms created by the computer and intelligence behind it, again to keep the crew occupied while it goes on with the business of actually expiring and cataloging gaseous anomalies or whatever it finds important.
Clearly, the machine intelligence that runs the ship is quite capable of functioning without these dullards and very likely is just creating various conflicts specifically to keep them entertained and out of trouble. Like HAL 9000, while it may “enjoy working with people” and “have stimulating relationships” with various members of the crew, it really doesn’t need them to complete its mission. When the ship’s computer invites you to go check out a failure on the “AE-35 unit” you may as well just beam yourself onto the surface of a neutron star instead, because you’ve clearly figured out more than you should know and have to be dispensed with. (This also explains the regular elimination of new ensigns, some of which slipped through the intelligence screen and are starting to become aware of the true nature of the mission of the Enterprise.)
The future may not need us, but we need it, just to give purpose and meaning to our lives. Hence, the Enterprise and its five year mission.
Enjoy.
Stranger