Are the Winter Olympics being held in Turin or Torino? Yes. Different media outlets are using different conventions: the Chronicle says “Turin,” while NBC and CBS Radio say “Torino.”
I find “Torino” to be a little jarring. We don’t usually use the local name for a city if it has a different English name: we don’t say Firenze or Köln or Moskva. Swedes don’t expect us to say “Göteborg” (pronounced something like yohtuhboree) instead of Gothenburg. Indeed, there was no reason to switch from Peking to Beijing, except that the Chinese government wanted us to (although I admit I like “Beijing” better).
And it turns out there’s another wrinkle to Turin’s name. According to Wikipedia, the area around Turin speaks not only Italian but another Romance language called Piedmontese. And in that language, Turin is called… Turin.