In Back to the Future: Part II, Doc Brown discovers that the McFly family is destroyed in the future, and it can all be traced back to Marty, Jr. agreeing to some proposition by Griff and his gang. So, Doc goes back to 1985 and recruits Marty to help him prevent that event from happening, which they succeed in doing.

The problem is, if they prevent the incident from occurring, how does Doc Brown know about it in the first place? The ripple effect would inevitably catch up to Doc Brown and he would have found that all is well with the future McFlys and presumably would not have investigated further. Paradox!