I think the ideal situation is to have a single, comprehensive question that covers all the variations. An ideal answer would be something along the lines of:
There were 36 total romantic affairs, three of which took place in the movies (2 in the same movie!), 18 in the original TV series, one in ST:TNG (!), and 14 in various novels. The list is as follows (aliens are denoted with a *):
To that end, I propose that Kevin Howell's version of the question be edited (with his approval, of course) to read:
How many women has Captain Kirk slept with?
It's an on going punchline that Kirk banged his way across the galaxy.
Is it actually based on fact though? In the TV series and movies, how many actual women did Kirk boldly go into with his Enterprise? (pun intended). Please distinguish aliens from humans, for those who are curious, and also indicate which are from the TV series and which are from movies.
The only woman I know for sure he Zap Brannigen'd was the lady who had his son.
Normally, I would suggest that the first question be kept, but since the OP of that question has disassociated/deleted their account, I think it appropriate to keep the reputation gains for our currently active members.
I'm not certain whether novels should be included in that list or not; DVK's answer seems to have a pretty good source on instances within the novels, so maybe they should.