Why does the LDS church  (Mormon) put so much more emphasis on the family than most other denominations do? Why do Mormons put so much more emphasis on the family than most other denominations do? What about their doctrine causes this? Or is it more because of culture/tradition?
I'm answering this only because of the year I spent in a Mormon (LDS) church.  If anyone who is LDS would like to post a different answer, please do.  This is based only on what I observed and learned during that time.

There are actually a few reasons for the emphasis on family.  The first section below is presented to add emphasis to the "meat" of the answer found later on.

The first has to do with the fact that LDS doctrine teaches that you have to add works on top of the free salvation presented by Jesus' sacrifice if you want to attain to the highest level of Heaven (also referred to as the highest degree of glory.

This underlies a lot of why members of the LDS Church are such stellar examples of how to behave, or at least why so much emphasis is put on "being good".  Doing the will of God and actually following the commandments is seen as necessary to achieve the highest level of glory.  One of the basic principles of the LDS Church is that other denominations are false, because Christianity went into full apostasy.  They view the concept of salvation by grace through faith apart from works as a false doctrine that encourages people to continue sinning while believing they are saved.  I can't tell you how many times I heard Matthew 15:8 quoted in Sunday Schools and in services.

The emphasis on being a good person springs from this belief.  This is, from what I've experienced, the most crucial aspect of LDS doctrine, and the belief that good works are necessary to future glory underlies a great deal of the emphasis on goodness.  Part of the emphasis on family springs from this.  Quite obviously, it is good to love your family and to have a close family.

Their teachings also include the idea that your family life continues on in heaven, and they want to be able to spend eternity with their families. This  feeds the emphasis on family, because close families are less likely to drift away from the Church. Since the view is that a person who leaves the Church is going to attain a lower level of glory, they want very much to maintain close ties to keep their children and loved ones in the fold.  The best way to do this is to encourage family time, and closeness in the family.

You can read the official LDS statement on the importance of family  while a more "evangelical" and less "doctrinal" explanation can be found here.