"The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex.
Congress shall have power to enforce this article by appropriate legislation."
After years of frustration when women's rights advocates had argued that the preceeding amendments granting suffrage regardless of race should include the same regardless of sex, finally a proposal was drafted and sent to the senate for consideration in 1878. The senate did not even vote on the proposal until 1887, at which time it was rejected by a vote of 16 to 34. At the beginning of the 20th century, however, women's rights again became a hotbed issue and suffragettes won support in many states, especially in the west where several states passed legislation granting "partial suffrage".
On August 18th, 1920, after much urging from President Wilson and a special session of Congress, it finally passed and was ratified by the states. Despite this it was not until the 1950s that women began to vote in large numbers whereas today, statistically, more women vote than men, especially in the 18-24 age range.
Other countries where women can vote include:
Isle of Man (since 1881)
New Zealand (since 1893)
South Australia (since 1895), Australia entire 1902
Finland (since 1906)
This list is by no means exhaustive, and there are some places in the world, like Saudi Arabia, where suffrage for women and men is severely limited or non-existant, but steps have been taken to see that it is eventually granted.