Imagine if you go back to the Kennedy assassination, and can't resist the urge to shout a warning, only to find it was him turning to hear what you were shouting that brought him in line with a bullet that would have otherwise missed.
That would likely be the
predestination paradox which is a situation in which a person traveling back in time with the intention to change the outcome, becomes part of past events. An example of this is in the Dr Who story 'Rosa' in which the Doctor & her companions realise at the last moment on the bus that they're now part of the events they learnt about in school.
The short lived
Buck Rogers in the 25th Century in 1979-80 did a story about a time traveller from the past who turns up in the 25th Century but on returning to the past, leaves a message for Buck in which he reveals that the discovery of time travel and his journey into the future being made public were responsible for triggering WW3 in the first place.
Another fun time travel story is the ST TNG episode
'Cause and Effect' in which the crew discover they're stuck in a time loop and plot how to escape.