What did they stand for?
This is a liste of a little inf. on the prophets of our time.  You can find a LOT MORE at "http://www.lds.org", go to the Church Magazines. Search “The Friend” and you'll find some useful info and biographical of most of the prophets of out time. 

 
Joseph Smith Love others, even our enemies as well as our friends. Be brave
Brigham Young  Truth is obeyed when it is loved 
Obey the Word of Wisdom.
John Taylor The gospel whispers peace. Be a valiant missionary
Wilford Woodruff  We need to be guided by the Spirit of God. Follow the Prophet.
Lorenzo Snow The time came when he was prophet to do the will of the Lord and to pay him and honest and hull tithing. Pray and know that prayers are answered
Joseph F. Smith Forgive all men. Have courage
Heber J. Grant I assert with confidence that the law of success, here and hereafter, is to have a humble and a prayerful heart, and to work, work, work. Be persistent - keep trying
George Albert Smith All the people of the earth are our Father's children. Have faith to be healed
David O. McKay Every member a missionary. Stand for the right
Joseph Fielding Smith The Church is a world church; the gospel is for all men. Study and memorize the scriptures
Harold B. Lee Keep the commandments. Listen to and obey the Spirit.
Spencer W. Kimball Lengthen your stride. Set hard goals and always do your best
Ezra Taft Benson Read and study the Book of Mormon. Have integrity.
Howard W. Hunter Go more often to the temple . Let us. treat each other with more kindness, more courtesy, more humility and patience and forgiveness. Work hard and be dependable
Gordon B. Hinckley Build small temples. Show kindness and concern for others