Answer:
The modern day Prophets of the Church of Jesus Christ of Latter-day Saints (the "Mormon" church) from 1830 to 2010 have been:
Joseph Smith, Jr.
Brigham Young
John Taylor
Wilford Woodruff
Lorenzo Snow
Joseph F. Smith
Heber J. Grant
George Albert Smith
David O. McKay
Joseph Fielding Smith
Harold B. Lee
Spencer W. Kimball
Ezra Taft Benson
Howard W. Hunter
Gordon B. Hinckley
Thomas S. Monson
The members of the First Presidency and Twelve Apostles are also considered prophets, but there have been too many to list here.