It can be even more fun to have them do things that seem counter-historical, but fit them into history. Your hero could, for instance, deflect Oswald's gun only to have JFK shot from the grassy knoll (thus explaining some of the inconsistencies in the official story), or shag Victoria and be the father of one of her children (find one that was strikingly different, or that she treated differently, and make that the reason). It's fun for the reader, as it becomes a get-out-of-that plot.