Why does Genesis record only 10 names from Adam to Noah? Genesis 5 (NIV)
  
  And Adam lived one hundred and thirty years, and begot a son in
  his own likeness, after his image, and named him Seth. After he begot
  Seth, the days of Adam were eight hundred years; and he had sons and
  daughters. So all the days that Adam lived were nine hundred and
  thirty years; and he died.
  
  Seth lived one hundred and five years, and begot Enosh. After he begot Enosh, Seth lived eight hundred and seven years, and had sons
  and daughters. So all the days of Seth were nine hundred and twelve
  years; and he died.
  
  Enosh lived ninety years, and begot Cainan. After he begot Cainan, Enosh lived eight hundred and fifteen years, and had sons and
  daughters. So all the days of Enosh were nine hundred and five
  years; and he died.
  
  Cainan lived seventy years, and begot Mahalalel. After he begot Mahalalel, Cainan lived eight hundred and forty years, and had sons
  and daughters. So all the days of Cainan were nine hundred and ten
  years; and he died.
  
  ......


Genesis 5 lists the genealogy of Adam as Adam, Seth, Enosh, Cainan, Mahalalel, Jared, Enoch, Methuselah, Lamech and Noah. Ten in all. Though each of these men had other sons and daughters, their names are not recorded.

Why are only ten names recorded and the rest are ignored?

Does this imply that these ten men were more important than others?
Noah's Lineage

Noah was definitely a significant figure, as it was he and his family alone who survived the flood.  The purpose appears to be to show Noah's lineage from Adam.  Adding in brothers and sisters at each level would be a bit tangential to that purpose.

Enoch was certainly a man of note due to his close relationship with God.  

The Line of Cain

Genesis 4 tells us about both Cain and Abel, who were indeed brothers of Seth.  This chapter also gives us the line of Cain as follows:

Cain > Enoch > Irad > Mehujael > Methushael > Lamech.

Lamech's two wives were Adah and Zillah.

Adah bore Jabal and Jubal.

Zillah bore Tubal-cain and his sister Naamah.

So, we are actually given other names in the line of Cain in Genesis 4, even though both Cain and Lamech were murderers.  The line of Noah does seem to be a more righteous line, to be sure.

The Second Gospel

There is another interesting idea that has been put forward, specifically that the meanings of the ten names in Noah's lineage have significance--sort of a Second Gospel:

Adam        Man
Seth        Appointed
Enosh       Mortal
Kenan       Sorrow
Mahalalel   The Blessed God
Jared       Shall come down
Enoch       Teaching
Methuselah  His death shall bring
Lamech      The despairing
Noah        Rest, or comfort


Put together, this could be as follows:


  Man is Appointed Mortal Sorrow.  [The Blessed God] [shall come down], teaching.  [His death shall bring] to [the despairing], [rest (or comfort)].