Whenever I've thought about this, I've always wanted to really stir the anthill.

[no killing - no prevention of some event that you really don't like]

How much could one person do, at the right time?

What would have happened if someone from our time, with our knowledge of history, had assisted Hannibal's invasion of Rome during the Punic Wars? He probably could have won if he had assaulted the city immediately, instead of waiting for Scipio Africanus. Was Rome such an immense and unique builing block of modern civilization that we wouldn't have internal combustion engines?

Could Phoenician society have survived the barbarian invasions?

Could an industrial revolution like they saw in England in the 17-1800s have started in Hellenistic Greece/Persia? They were pretty inventive, and if memory serves me correctly that is when the water screw was developed.

Since it didn't happen, even with that culture, I assume that it could not have. Why not? Did they not have enough math, did they not have the right level of technology? Did they have too cheap of human labor? (Something which the Americas /definitely/ did not have).

What if, centuries before Christ, you built a big-ass highway between Native American cultures in the Northeastern United States, Central America, and Peru? The cultures could have shared technology and local their local providences (llamas, wheels, foods?) and shared diseases and may or may not have been able to resist the European diseases.

Would we still be living in thatch huts? What would have happened?

I would go back in time and bring the sports almanac with me. :D

That somehow sounds familiar...you could almost make a movie about time travel where someone brings a sports almanac back in time and then perhaps travels back to the future. hmmmm