The Time Traveller's Wife And The Time Patrol

If you had travelled into the past and wanted to be as sure as you could of returning to your remembered "present," then you would have to avoid altering any past events. One theory is that, on returning futureward, you would revert to your original timeline in any case but that is not what happens in Poul Anderson's Time Patrol series. For an excellent example of an apparently changed past, read Audrey Niffenegger's The Time Traveler's Wife. 

Henry sees Clare complete a picture and begin to sign it but tells her not to sign it because he has seen it unsigned in the future. She signs it. Returned to his "present," he looks for the picture. It is not on the wall above the fridge where it should be. It has slipped down behind the fridge. He retrieves it. It is unsigned. Then he notices that the bottom of the sheet has been trimmed off. He asks Clare. She had decided to play it safe and had trimmed off the signature.

If Clare had been the sort of person who would not have trimmed off the signature, then the picture would have remained signed and Henry would have seen it signed so he would not have told Clare not to sign it and she would have signed it.