Starting in 1910, some states in the Western part of the United States began to extend the vote to women for the first time in almost 20 years. (Idaho and Utah had given women the right to vote at the end of the 19th century.) Still, the more established Southern and Eastern states resisted. It wasn't until today, 93 years ago, that all American women were able to vote.
On Election Day in 1920, millions of American women exercised their right to vote for the first time. It took activists and reformers nearly 100 years to win that right, and the campaign was not easy: disagreements over strategy threatened to cripple the movement more than once. But on August 26, 1920, the 19th Amendment of the Constitution was finally ratified, enfranchising all American women and declaring for the first time that they, like men, deserve all the rights and responsibilities of citizenship. See http://www.history.com/topics/the-fight-for-womens-suffrage.
Suffrage for women in other countries came earlier: New Zealand (1893), Australia (1902), Finland (1906), Norway (1913), and Denmark and Iceland (1915), Canada (1916-1940), the Union of Soviet Socialist Republics and the Netherlands (1917), Austria, Czechoslovakia, Poland, and Sweden (1918), and Germany and Luxembourg (1919).
Suffrage for women in some countries came later: Ecuador (1929), Spain (1931), Brazil (1932), Philippines (1937), El Salvador (1939), Dominican Republic (1942), France (1944), Guatemala and Japan (1945), Belgium, Italy, Romania, Yugoslavia and Argentina (1946), China (1947), Indonesia (1955), Switzerland (1971), and Liechtenstein (1984).
In African countries men and women generally received the vote at the same time. In many Middle Eastern countries universal suffrage was acquired after World War II. In some countries, such as Saudi Arabia, there is no suffrage at all, and in others, such as Kuwait, it is very limited and excludes women completely. See http://teacher.scholastic.com/activities/suffrage/history.htm.