Well, this was taken from the series, but the definitive Captain Kirk movie, would in my opinion, have to be Star Trek VI: The Undiscovered Country, one of the better movies.
Song, heh, Mr. Tamberine Man - As great as he was as Denny Crane and always brilliant as Captain Kirk, when he covered Mr. Tamberine Man, I was embarrased - now here's the link! But first, unless you know it well enough, listen to the original first for atleast 30 seconds, then watch William Shatners darkest moment - I'm sorry Bill we love you man! (Also, can I post these? other people have posted Youtube, so I guess I can).
Bob Dylan - Tambourine Man: http://www.youtube.com/watch?v=hGE1uGt3ng8 (Not a huge Bob Dylan fan, so if this isn't the original, hopefully its close enough)
William Shatner - Mr Tambourine Man: http://www.youtube.com/watch?v=_0hTtsqiFCc