Here's a list of different time travel movies or shows that I've seen and how it effects the time line. Please note that when I refer to internal time travel, it means the time traveller is travelling within their own body and thus can only travel between their birth and their death (therefore no possibility of running into your other self). External is like BTTF where the characters can travel to any time and therefore could co-exist with other versions of themselves.
SPOILERS AHEAD
13 going on 30: Lead character travells forward in time internally from the age of 13 to the age of 30. Near the end she does travel back to the age of 13 again and makes different life decisions based on her knowledge of the future. At the very end is shown as a 30 year old with a different future.
Austin powers movies; second and third films involve time travel but no characters attempt to change the timeline.
Bill and Ted films; characters get messages and even items planted for them by their future selves thus implying time travel has always been in the timeline. Villains attempt to change the timeline but are unsuccessful.
buttefly effect; character travels back in time to various points in his past and usually comes back to a different future each time he does so.
a christmas carol; lead character goes to the past, present, and future. While we are unsure if he is able to change his future, it is presumed the future he sees is the one that would transpire if he does not change his ways.
click; lead character is able to travel back in time but merely as a spectator, he is invisible to other people and doesn't seem to be able to physically move things and thus proably cant change the past. Character does have the ability to speed up time and thus essentially travel to the future
frequency; no characters travel through time but a man is able to speak to his father 30 years earlier via radio and give him information about the future which does in fact change the timeline. This is a good example of how effects on the timeline effect human memory; when the past changes, the son remembers both timelines, the previous one and the new one.
hot tub time machine (great BTTF spoof btw); 4 characters travel back to 1986, 3 internally, 1 (who was not born yet in 1986) externally. The timeline gets changed, 1 character stays back in 1986 but the other 3 return to a different future
peggy sue got married: lead character travels back in time 25 years internally and at the end returns to a different future
terminator films; plays with both time travel theories; in the first film, john connor sends kyle reese back from 2029 to 1984 and while in 1984, impregnates johns mother thus becoming johns father (john was born in 1985) so this would imply the timeline always expects time travel. Terminator 3 does indicate that events of terminator 2 posponed a judgement day which was supposed to happen in 1997 to the early 21st century. This implies that the timeline expects time travel but can still be changed to an extent
the time machine; lead character builds a time machine to save his fiances life, every time he goes back to save her, she dies a different death. So the events can be changed but the ending effects can not be.
the time travellers wife; character involuntarily travels to the past and the future but seems the timeline expects time travel as he is unable to change events (ie his mother died in a car accident and despite attempting, does not have the ability to save her)
timecop; time travel exists but only to the past, travel to the future is impossible because the future hasn't happened. The timeline is changed several time and the movie has a rule that the same matter can not occupy the same space at the same time. Meaning you cant go back in time and touch yourself. This does eventually happen and both versions of the character evaporate (which should cause a paradox but doesnt.)
being erica (canadian TV show): lead character is given time travel therapy where her doctor allows her to go back in time (and once to the future) to relive past events. He tells her she is not allowed to make drastic changes (a murky subject which I'll get to later); so for instance on the day she loses her virginity, she travels back and still loses it but to a different person. The character usually travels internally except if she travels to before her birth in which case she travels externally. Her doctor usually travels with her in an external manner (so she always looks the way she did in whatever year she's travelled to unless she goes to before her birth while he always has the same appearance). In one episode she travels back and saves her brothers life despite being instructed not to do so, returns and finds him alive in the present but he dies again upon her return and she chooses to go back and fix her changes.
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