In all iterations of Star Trek, (TOS, TNG, DS9, VOY, ENT and the movies) how many transporter accidents or incidents, integral to the plot, have there been?
Based on the criteria that an accident must occur and that it must be integral to the plot (e.g mentioned repeatedly or main plot driver), there are surprisingly few "transporter accident" episodes, only one or two per show.
For completeness, I've also lumped in those episodes where intentional abuse of the transporter occurs as the main plot driver
Rascals - Transporter accident: Age regression
Realm of Fear - Transporter accident: Personnel trapped in matter stream
Second Chances - Transporter accident: Life creation
Data's Day - Transporter abuse: Faked death
The Next Phase - Transporter accident: Personnel trapped out of phase
Our Man Bashir - Transporter accident: Personnel trapped in buffer
Through the Looking-Glass - Transporter abuse: Travel to Mirror Universe
Shattered Mirror - Transporter abuse: Travel to Mirror Universe
The Emperor's New Cloak - Transporter abuse: Travel to Mirror Universe
Field of Fire - Transporter abuse: Murder
Star Trek: The Motion Picture - Transporter accident: Death in transit x 2