who was the first woman to run for president of the US and when did she seek office?

Answer 1

Victroria Woodhull ran for the presidency in 1872. It was not legal for her to do so, as women did not have the right to vote. But she did run for office.
http://en.wikipedia.org/wiki/Victoria_Woodhull
http://www.victoria-woodhull.com/

Belva Ann Lockwood is also an early claimant. She ran in 1884 and 1888 on the Equal Rights ticket.
http://www.stanford.edu/group/WLHP/papers/lockwood.htm
http://en.wikipedia.org/wiki/Belva_Ann_Lockwood

In the modern era, the first woman to run for president was Rep. Shirley Chisholm. PBS did a documentary on her candidacy:
http://www.pbs.org/pov/pov2005/chisholm/
http://en.wikipedia.org/wiki/Shirley_Chisholm

Here is a Wiki-list of women who have run for president. Most are from left-of-center parties:
http://en.wikipedia.org/wiki/List_of_female_United_States_presidential_and_vice-presidential_candidates

Answer 2

Margaret Chase Smith was nominated for president by the 1964 Republican National Convention. But Victoria Claflin Woodhull became the first woman presidential candidate in the United States in 1872 when she is nominated by the National Radical Reformers with Frederick Douglass as running mate.
source: http://www.infoplease.com/spot/womensfirsts1.html

Answer 3

Right now - with Hillary Clinton. Geraldine Ferraro ran for vice president with Walter Mondale as the presidential candidate in the 1984 election, but were beaten by Ronald Reagan and George H.W. Bush (sr.)

Answer 4

Geraldine Ferraro ran for Vice with Walter Mondale for the President. This was during the 80's. They lost.

Answer 5

Most people would say Victoria Woodhull in 1872 though some dispute the validity of her candidacy.