The Star Trek: The Original Series and William Shatner's On-screen Journey
How many episodes of Star Trek: The Original Series did William Shatner not appear in? This question can be easily answered by a quick glance at Shatner's TV credits on IMDb, but the answer depends on how you interpret the series' unique episodes.
Shatner's Involvement in The Original Series
According to the records on IMDb, the original series of Star Trek: The Original Series comprised 79 episodes. However, it's worth noting that the final episode in the series was a two-part episode, "The Menagerie," which counts as a single episode. In all 79 of these episodes, William Shatner played Captain Kirk and appeared for a few seconds as his dead brother, Sam, in the episode "Operation: Annihilate!"
The Pilot: "The Cage"
Before the official start of the series, a pilot episode titled "The Cage" was created, which was later aired in 1987 as part of the Star Trek: The Next Generation (TNG) time slot during a writers' strike. In "The Cage," William Shatner portrayed Captain Christopher Pike, while Leonard Nimoy reprised his role as Spock and Majel Barrett played "Number One" and Nurse Chapel. Interestingly, most of the content from "The Cage" was later recycled and used in "The Menagerie."
A Closer Look at the Pilot
Note that while "The Cage" was never officially part of the Star Trek: The Original Series canon, it does provide insight into the backstory and early version of the show. If "The Cage" is counted, then Shatner did not appear in one episode. On the other hand, if it's not considered as part of the official series, then the answer is clear: Shatner appeared in every episode of the series.
Indisputable Facts
However, there is one indisputable fact. The only episode of The Original Series in which someone other than William Shatner played James Kirk (not counting stunt doubles) was the final episode, "Turnabout Intruder." In this episode, Sandra Smith played a scientist who used alien technology to switch bodies with Kirk. Thus, for the vast majority of the series, William Shatner was the only actor to play Captain James T. Kirk.
Conclusion
Whether you consider "The Cage" as part of the series or not, the answer to the question of how many episodes William Shatner did not appear in can be definitive. For a true "Star Trek" fan, the answer is simple, and it's a testament to Shatner's enduring legacy in the series.