Captain Kirk's journey, in order
To watch Captain Kirk's story in order, start with The Original Series: Season 1, then The Original Series: Season 2 and The Original Series: Season 3. That's 12 out so far, about 89 hours, ending with Generations.
William Shatner played Captain Kirk for three seasons of television, an animated series and seven films. This is his story in order, with Chris Pine's Kelvin timeline Kirk as an extra.
Updated
Captain Kirk's story in order
The Original Series: Season 1
Kirk commands the Enterprise on its five-year mission.
The Original Series: Season 2
The Original Series: Season 3
The Animated Series: Season 1
The mission continues, animated.
The Animated Series: Season 2
The Motion Picture
Admiral Kirk takes back the Enterprise.
The Wrath of Khan
An old enemy returns, and Kirk faces loss.
The Search for Spock
Kirk risks everything for Spock.
The Voyage Home
The crew travels back to 1986.
The Final Frontier
A search for God at the centre of the galaxy.
The Undiscovered Country
Kirk must make peace with the Klingons.
Generations
Kirk meets Picard.
Also worth watching
Star Trek (2009)
Chris Pine as a young Kirk, in an alternate timeline.
Star Trek Into Darkness
Star Trek Beyond
Questions
What order should I watch Captain Kirk's story in?
Start with The Original Series: Season 1, then The Original Series: Season 2 and The Original Series: Season 3, and follow the list above: 12 in all, ending with Generations.
How long does it take to watch all of Captain Kirk's story?
About 89 hours for the 12 out so far.
Do I need to watch the original series before The Wrath of Khan?
It helps to have seen 'Space Seed', the Season 1 episode that introduces Khan. The film is its sequel.
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