There is an excellent article called "Extending Institute" by Elizabeth VanDenBerghe in the October 97 Ensign p. 38 the abstract is as follows:

"Since LDS institutes opened their doors to those not enrolled in colleges and universities, growing numbers of young adults have found the rewards of gospel classes, good fellowship, and institute activities."

The following quotes are all from general conference within the last 20 years:

Elder L. Tom Perry:
("Receive Truth", The Ensign November, 1997, pg 62- conference address about beginning of Seminary & Institute)

        "Plan on completing the full four years of seminary.  You know the institute is available for all students and nonstudents between the ages of 18 and 30. Are you enrolled?  If not, I invite you to take advantage
of this wonderful opportunity. And to you who are enrolled, study diligently to learn the gospel.  I promise you that the foundation you receive in these two great programs will bless you throughout your lives.  This is my witness to you in the name of our Lord and Savior, even Jesus Christ, amen."
 

"To Be Learned Is Good If..." -  Elder Boyd K. Packer (October Gen. Conf. 1992)  (link)

        "Those who cannot attend Church schools have been counseled by the First Presidency to gather where there is an institute of religion.  The institute program will be greatly enhanced for your benefit."
 

"The Library Of The Lord" -  Elder Boyd K. Packer   (April 1990  Gen. Conf.)   (link)

        "All of these courses in seminary, in institute, and at Church schools are taught by dedicated teachers.  They deserve our respect, our deep gratitude, and our full support.  Every parent, every Church leader,
should act as an enrollment agent for seminaries and institutes.  Parents and priesthood leaders check on your college students.  See that they attend the institute."
 

"Godly Characteristics of the Master": President Ezra Taft Benson (October Conf. 1986)

        "We must balance our secular learning with spiritual learning.  You young men should be as earnest in enrolling in seminary and learning the scriptures as you are in working toward high school graduation.  Young adults enrolled in universities and colleges or other postsecondary training should avail themselves of the opportunity to take institute of religion courses or, if attending a Church school, take at least one religion course every term. Joining our spiritual education to our secular learning will help us keep focused on the things that matter most in this life.  Though I am speaking to you priesthood holders, the same admonition applies to the women of the Church as well as to the men."
 

President Spencer W. Kimball said it this way:

        "Youth, beloved youth, can you see why we must let spiritual training take first place?--Why we must pray with faith, and perfect our own lives like the Savior's?  Can you see that the spiritual knowledge may be
complemented with the secular in this life and on for eternities but that the secular without the foundation of the spiritual is but like the foam upon the milk, the fleeting shadow?  Do not be deceived  One need
not choose between the two but only as to the sequence, for there is opportunity for one to get both simultaneously; but can you see that the seminary courses should be given even preferential attention over the high school subjects; the institute over the college course; the study of the scriptures ahead of the study of man-written texts; the association with the Church more important than clubs, fraternities, and
sororities; the payment of tithing more important than paying tuitions and fees?"
 

"Agency and Control", April 3, 1983 Gen. Conf. address by Boyd K. Packer   (link to talk)

        "Without guidance, your student may choose another elective instead of seminary, or another course instead of an institute class.  That would surely be a mistake.  It would be like adding one more brick to the house of knowledge when there is little mortar to hold it all together.  Parents, encourage, even insist, that your students register for seminary or institute.  Presidents, bishops. youth leaders, you are responsible to encourage every youngster, without exception to enroll.  Few things you do will benefit them quite as much.

        "Students, if your values are in place, you will not hesitate to forego an elective class that may decorate your life in favor of instruction which can hold together the very foundation of it.  Then, once enrolled, attend, study and learn.  Persuade your friends to do the same.  You will never regret it; this I promise you."
 

"Prepare Now For Your Mission": Elder J. Thomas Fyans (April 1977)

 5. Be active in the Church. This means attendance at Sunday School, priesthood meeting, and sacrament meeting and involvement in Scouting, seminary or institute, depending upon your age.

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        "Secular knowledge, important as it may be, can never save a soul, nor open the Celestial Kingdom, nor create a world, nor make a man a God….Can you see why we must let spiritual training take first place?….One need not choose between the two, but only as to the sequence, for there is opportunity for one to get both simultaneously….Seminary and Institute courses should be given preferential attention….the study of the scriptures ahead of the study of the man-written texts."

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        "I know the power that comes from associations in the seminary and institute programs.  It has enriched my life, and I know it will do the same for you.  It will put a shield of protection around you to keep you free from the temptations and trials of the world.  There is a greater blessing in having a knowledge of the gospel.  And I know of no better place for the young people of the Church to gain a special knowledge of sacred things than in the institute and seminary programs of the Church."   (The Ensign, November 1997, pp 61-62

        "Plan on completing the full four years of Seminary... Study diligently to learn the gospel.  I promise you that the foundation you receive... will bless you throughout your lives.  This is my witness to you in the name of our Lord and Savior even Jesus Christ."

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Pres. Gordon B. HInckley:

        "Our great program of the Church education moves forward.  The work of training students through the Seminary and institute program is constantly being enlarged... We urge all for whom it is available to take advantage of it.  We do not hesitate to promise that your knowledge of the gospel will be increased, your faith will be strengthened, and you will develop wonderful associations and friendships."

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President Benson:

      "Give me a young man who has kept himself morally clean and has faithfully attended his Church meetings.  Give me a young man who has magnified his priesthood and has earned the Duty to God Award and is an Eagle Scout.  Give me a young man who is a seminary graduate and has a burning testimony of the Book of Mormon.  Give me such a young man, and I will give you a young man who can perform miracles for the Lord in the mission field and throughout his life."

        "Yes, give me a young woman who loves home and family, who reads and ponders the scriptures daily,
who has a burning testimony of the Book of Mormon.  Give me a young woman who faithfully attends her
church meetings, who is a seminary graduate, who has earned her Young Womanhood Recognition Award
and wears it with pride!  Give me a young woman who is virtuous and who has maintained her personal
purity, who will not settle for less than a temple marriage, and I will give you a young woman who will
perform miracles for the Lord now and throughout eternity."

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"Regularly attend seminary and be a seminary graduate.  Seminary instruction is one of the most significant spiritual experiences a young man can have."

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"The Church periodically checks the pulse and measures the progress of the institute programs.  This last year an institute study reveals the following:

...of those graduating from institute, 96% received temple endowments; 98% of those receiving their endowments had their marriages performed in the temple; 96% of the men graduating from institute served missions"

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Quoted in Vaughn J. Featherstone's new 1999 book:  The Millennial Generation--Leading today's youth into the future, p. 101:

Elder Packer:  "In the history of the Church there is no better illustration of the prophetic preparation of this people than the beginnings of the seminary and institute program.  These programs were started when they were nice, but were not critically needed.  They were granted a season to flourish and to grow into a bulwark for the Church.  They now become a godsend for the salvation of modern Israel in a most challenging hour.  We are now encircled.  These are the last days, forseen by prophets in ancient times."  (Teach the Scriptures)
( SLC: Church Educational System, 1978)

 Elder Neal A. Maxwell has said: "I'm not sure our young people can survive spiritually today without seminary."