Keep in mind there's close to 600 hours of TV and film here. If you're taking in one or two episodes every day, you're still looking at over a year of "Trek." If you're looking to pare that down to something a little more reasonable, you should absolutely feel free to use a skip guide. Some episodes are just plain bad — don't torture yourself.
Here's the watch order:
Star Trek: The Original Series
The Animated Series
Star Trek: The Motion Picture
Star Trek II: The Wrath of Khan
Star Trek III: The Search for Spock
Star Trek IV: The Voyage Home
Star Trek V: The Final Frontier
Star Trek VI: The Undiscovered Territory
The Next Generation Seasons 1-7
Star Trek: Generations
Deep Space Nine Seasons 1-5
Voyager Seasons 1-2
Star Trek: First Contact
Deep Space Nine Seasons 6-7
Star Trek: Insurrection
Voyager Seasons 3-7
Star Trek: Nemesis
Star Trek (2009)
Star Trek: Into Darkness
Star Trek: Beyond
If you're not sure that a little '60s campiness is your thing, you can start with "The Next Generation" and loop back around to "The Original Series" later. This might seem like heresy to some, but "The Next Generation" is a lot closer in feel to modern television than "The Original Series." While the difference in presentation and production values shouldn't stop you from watch the best of original "Trek," it might be enough to turn off a complete newcomer.
Also, you're definitely better off if you have some appreciation for what the characters from "The Original Series" are like before you watch the movies in the "Kelvin" timeline that begins with 2009's "Star Trek." That way, you'll be able to pick out what's different about their personalities and what's stayed the same. "Beyond" has a few references to "Enterprise" in it, but for the most part the "Kelvin" films don't really tie much into the shows made after "The Original Series."
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