Catholic Church - What happens when a married couple will never have sex? Let's say that they just do not want to have sex for some reason after the wedding. 
Does it mean that their marriage can be annulled by the Catholic Church even if they were married for 10 years?
In the general case marriage requires consummation, but the Catholic Church allows an exception which is called a "Josephite Marriage."  This is the kind of marriage that the Catholic Church believes Mary and Joseph entered into: a marriage without sex.

Despite the fact that no consummation took place, a Josephite marriage is not intrinsically invalid.  Even so, a marriage that has never been consummated would be more easily exited than a marriage that has been consummated.  Indeed the condition of consummation goes hand in hand with indissolubility.  If a marriage is consummated, it is indissoluble.  If it is not consummated, it is dissoluble.  Whether or not it is consummated, the marriage exists.

Dissolution of a marriage is actually different from annulment of a marriage.  Annulment says the marriage never existed; dissolution means that a partial marriage is being dissolved.  If a marriage is ratified and consummated then there exists the possibility of annulment, but not the possibility of dissolution.  If a marriage is ratified but not consummated then both the possibility of annulment and dissolution exist.


  Canon 1141 explains the Church's theological understanding of the
  significance of the consummation of a valid marriage: a marriage which
  has been ratified and consummated (ratum et consummatum) cannot be
  dissolved by any number power, or by any cause other than death.  If a
  couple have been validly married, and have consummated their
  marriage, the Church holds that their marriage is indissoluble. 
  Period.
  
  But if the couple were validly married, yet had never consummated
  their marriage--a marriage ratum sed non sonsummatum, in other
  words--the situation is theologically quite different!  Such a
  marriage can be dissolved by the Roman Pontiff for a just reason,
  at the request of one or both parties to the marriage (canon
  1142).  A ratum sed non consummatum marriage is not
  indissoluble, because the indissolubility of a valid marriage comes
  about through its consummation.
  
  -Canon Law and Consummating a Marriage