This has always been an awesome POD. Not just because I, like most on this forum, don't like Woodrow Wilson but also because a Hughes victory in 1916 could dramatically alter the course of history. If Hughes won in 1916 and enters the war but is saddled with the domestic headaches faced by Wilson (riots, strikes, economic depression), it's likely that the Democrats win in 1920. And if Wilson wins the popular vote in 1916 but loses the electoral vote, it's quite possible that like Cleveland he'll make a comeback four years later. This means the Democrats are in power during the Roaring Twenties and probably the Great Depression as well, paving the way for the GOP to win in 1932. Without FDR's 1932 victory and his New Deal coalition, this could mean that the Democrats remain the more Conservative party and the GOP is more liberal. On the other hand, if Republican policies aren't enough to relieve the Depression (the GOP would still have the strong reactionary element that stymied TR's more liberal policies in his second term) then it's possible that a third party lead by Huey Long takes power in 1936 or in 1940. The Prospect of a Long dictatorship is truly a frightening one. I for one am very glad we never went down that path.
Smaller butterflies would include the end of the lame duck period. Wilson planned on appointing Hughes SecState and then resigning along with his VP, making Hughes the President a few months early. Also, Hughes supported a League of Nations and unlike the uncompromising Wilson he would be more willing to make amendments to the Treaty of Versailles in order to get it passed. This would mean the U.S. is a member of the League and could take some diplomatic action against Hitler and/or Mussolini and perhaps Franco. The problem is that the leading member nations (UK and France) would still refuse to confront fascism as in OTL until it's too late. Not to mention that the U.S. public, while supportive of the Allies, was overwhelmingly isolationist until Pearl Harbor. So it's unlikely that WWII would be prevented, but US membership in the League would certainly be a positive.