What is the most influential newspaper in the world?

Impossible question to answer. In the U.S., good options are the New York Times (related is the International Herald Tribune) and the Washington Post. The U.K. offers the Guardian and the Times. France offers le Monde. This is only from my limited perspective, I'm sure other countries with a free press have wonderful options, and they are each going to have their own slant.

Additionally, though its not a newspaper, Al Jazeera (and related Al Jazeera English) provides great coverage from its own perspective. The best option is to take in as much as you can, and make your own choice.