This is a difficult question to answer, only because it is only as influential as another country lets it be. For example, China is less influenced by American culture than England is. This is because China has made it really hard for anyone to get into China’s popular culture unless they tow the party line. England, on the other hand, has an open market and lets the market dictate what’s popular.
All this said, what is going on in America and with the president’s relations with other countries can make a difference in how influential America is in specific open market countries. Some see America as a big bully. Others see it as a good trading partner. It all depends on the political trends at the time.