The most recent one is "The Butterfly Effect", taking its name from the theory that the beating of a butterfly's wings could divert a hurricane, ie every change however small, causes a series of changes which could lead to a major difference.
This might be a bit too obvious but could this be 'Back to the Future'? I appreciate that Marty doesn't go back in time specifically to stop Doc from getting gunned down in the carpark but it does fit to a degree...
Frequency - would this be the one ? Dennis Quaid in it as the father back in the 1960s and his son contacts him from the 1990s via wireless that used to belong to his dad. His dad in the son's world is dead. Timeline gets played with, murderer gets caught, everyone lives happily ever after. If it isn't this one you were thinking about, watch it, we found it good !
What about It's a Wonderful Life? Not quite what you've described. In fact, it's almost the opposite, i.e, that it demonstrates the awful things that would have happened if the character Jimmy Stewart plays had never lived.