In the Terminator series of films, there is the John Connor and Kyle Reese loop. A future John Connor sends Kyle Reese back in time to save Sarah Connor, his mother. Interestingly, Kyle Reese ends up becoming John Connor's own father. Thus the paradox of a closed loop. Without complicating the matter with Skynet and the machines, the actions of John Connor and Kyle Reese then creates an endless time loop.
Sean Shaffer explains the paradoxes, including about the development of Skynet (which came first, the chicken or the egg) very well in Den Of Geek
It's worth reading the entire article.
The paradox that's created in the Terminator series is that Skynet is built because an already built Skynet sends back a machine that will ultimately be destroyed and become the basis for Skynet. The question here is which came first, the machine or Skynet? The same goes for John Connor's life. John Connor is only conceived because he sent his dad back to impregnate his mother. It basically goes back to the original question of what came first, the chicken or the egg?
It's also in these events that we not only see how taking out one part of the equation would equate to a whole another timeline, but it also shows us how closely connected John Connor and Skynet really are. To put it simply, Connor and Skynet can't survive without each other, almost like Harry Potter to Voldemort. Their legacies are so intertwined that taking one out would possibly ruin or enhance the other, but ultimately create a timeline that cannot be predicted.
Similarly, but even more complicated is the relationship between The Doctor and the Daleks. The Doctor has his own timeline as a time traveller, which doesn't follow the linear timeline of the Daleks history.