The meteor from that cataclysmic event billions of years ago - never happened. That would be fascinating. What happens to the world then, with all these species that went extinct from that meteor? How does it effect, our ancestors? How does it effect present time?
What if the continents remained as one whole (depending on what you believe about the theories)? Is the world more united as one continent, or are wars closer to home?
If ancient Rome never fell, does the entire world still believe in the pagan gods? Does science progress faster or slower? What about social values? Style? Fashion? Politics?
Ah! There's so many! I keep coming up with more. There's no way for me to choose. Fun question though. ^^ It'd be interesting to see what stories come out of these ideas.