In the map above, we've shown all possible international routes one can travel between countries that don't have a formal agreement with the United States for extraditing accused criminals. Flying from Moscow to Kiev is fine, but think twice before traveling on to Berlin; the German government signed an extradition treaty with the US in 1978.
Of course, these details haven't stopped Snowden, who flew to Hong Kong with top-secret details of US surveillance programs even though the city-state has had an extradition treaty with the US since 1996. Now in Russia, Snowden is thought to be bound for Ecuador, which has a US extradition treaty--first agreed to in 1872--but is friendly to political asylum claims.
The US has bilateral extradition agreements with 107 nations (pdf). That includes treaties signed under previous regimes, some more than a century ago. Cuba, for instance, signed one with the US in 1904, but the two nations now have no formal diplomatic relations, which is why Snowden could be safe flying to Havana.
Still, if you go by all the extradition treaties formally recognized by the US, the western hemisphere is effectively sealed off to fugitives, with the exception of flights between Aruba and Curacao. Better to hop around Asia, Africa, and Europe.