A lot of times, people will try to avoid fate OR will find a work around so that they get the best outcome possible. These are NOT those times. 

1. David Tennant's incarnation of the Doctor was told that he will hear 4 knocks and then he will die. In some episodes following this being told to him, he comes close to hearing four knock but never does. Eventually, when the season finale, The End of Time Parts 1 and 2 aired, people expected The Master to be the one to kill the Doctor. However, after surviving that calamity that happened, the Doctor finally hears the four knocks. As it turns out, it wasn't from some villain of the week. It wasn't from any of his arch enemies. It was from Wilfred Mott; a rather beloved character that go himself trapped in a glass cage. Only way to get him out was for the Doctor to lock himself in the other room and absorb all the radiation. 


2. Specifically in Terminator 2 and Terminator 3: Judgment Day, Sarah and John Connor try to stop Judgment Day from happening. That way, Skynet doesn't activate and the war with robots never happens. Unfortunately, despite their best efforts, Judgment Day still happens as it was always supposed to. John Connor was just meant to get to a fallout shelter so that he could survive the impending disaster and lead humanity to eventually winning the war against the machines. 

For more specifics, in Terminator 2, two terminators were sent back in time; one to kill John Conner and another to protect him. While Sarah, John, and the good Terminator defeat the bad Terminator and melt him in the end, with the good Terminator being dropped into the lava as well due to the inability to self destruct, Terminator 3: Judgment Day happens. John Connor and friends attempt to stop the US Government or whatever agency from activating Skynet. This fails, so the Terminator sent back in time in this movie sends John Conner and his future wife to a fallout bunker so that they can survive and lead humanity to victory.  

Mods, I couldn't think of anymore examples. Apologies in advance if this breaks any rules. 

The prophecy still happens, no matter what you try to do.