In the movie Terminator, Kyle Reese is known to be the father of John Connor (the leader of the resistance againts Skynet)
and the savior/lover of Sarah Connor (John's mother).
In a logical sense though, there is no way that Kyle Reese is the original father and here is why.
The Rule of time Travel
While time travel is science fiction and a theory, it doesn't stray off too much from logic. In order to travel through time one needs some sort of transportation through time. When someone goes back in to time, they create a time loop, this is an infinite cycle that goes on and on through time and space, unless someone breaks it somehow. But the loop wasn't always there, it had to start off at certain point in time. That Loop started when Kyle Reese traveled back to the past the first time around. What about before that?
In to the Future
Kyle Reese was born in the future where the machines had already taken over, he wasn't born then and John Connor already existed without him going into the past in the first place. That's why if you think about it now, Terminator: Salvation's plot is idiotic, because even if they killed Kyle, that wasn't going to stop John Connor from being born, because Kyle isn't the original father. John Connor sent Kyle back only to protect his mother without realizing that Kyle would become his new father the first time it happened. The first time that a terminator was sent to the past to kill Sarah Connor. So how does John know how to fight the machines?
Back Into The Past
In Terminator: Rise of the Machines it is revealed that John didn't lead the resistance all by himself for he had his future wife's help Kate Connor,
the daughter of Lieutenant General Robert Brewster Skynet's primary creator.
So even though John Connor learned how to fight the machines thanks to his mother, it was his wife who showed him how to destroy Skynet. Thus turning him into the Savior of humanity.
Who is John Connor's Father?
There are some suspects on who could be John's father, it could be the man who Sarah Conor was suppose to date, even though there was only his voice in the film, and is unnamed in the movie, he seems the most obvious choice. But it could also be her best (Ginger Ventura) friend's boyfriend(Matt Buchanan)???
Who knows if there was some sort of attraction towards one another??? Start your gossip on girls.
However I could not find any reliable proof on who is John's real dad. I think this will always be a mystery since they made the film on Kyle Reese being the father period , but who knows, maybe in the future we'll get our answers and finally see Skynet destroyed. Pfft yeah right.