Has Christianity ever come down in opposition of arranged marriages? Many cultures in many ages have practiced arranged marriages. I understand that in Jewish culture --at about the time of Christ-- arranged marriages were considered a normal way of life. Obviously if this was a religious value at the time Christianity probably had an opinion about it. Somehow today, many 'Christian' cultures do NOT practice arranged marriages (none in the west, only a few scattered ones elsewhere).

How did this happen? Is it a cultural issue that Christianity never held a position on or did the early Christian church take a stand against the Jewish custom? Was it Christianity and some doctrine that instigated this change, or just coincidence?
Yes, in general Christianity has worked against arranged marriages historically.

The Wikipedia article on marriage notes:


  With few local exceptions, until 1545, Christian marriages in Europe were by mutual consent, declaration of intention to marry and upon the subsequent physical union of the parties... As Christianity spread during the Roman period and the Middle Ages,
  the idea of free choice in selecting marriage partners increased and
  spread with it.


A History of Marriage in Western Civilization contends that the previous Greek, Roman, and Jewish traditions of arranged marriage were eroded by the Church's role - first, the focus on asceticism and not always being married, and then by the Church's view of marriage as a sacrament and wanting more say in the process (for example by saying they had the power to annul marriages illicit in some way).

This is of course not universal; despite Ethiopia adopting Christianity in 333 AD they are still moving out of the practice.

This makes sense; arranged marriage tends to depend on two things:


Women being seen as undesirable/commodities by the society
Marriage being seen as an economic transaction between two groups


Christianity has eroded the "women are lesser" argument historically (though imperfect in practice, Christianity's view of women is WAY higher than many other culture/religions) because of the insertion of both the concept of the individual's relationship with God resulting in marriage necessarily being a matter of individual choice - "if they want to stay chaste, they don't have to marry" - and the Church as a cultural force wanting part of the say in marriage for both religious and, frankly, political reasons. 

Note that there is also a major difference between arranged marriages that still (technically) require the assent of those being married, and forced marriages: 


  The Roman Catholic Church deems forced marriage grounds for granting
  an annulment — for a marriage to be valid both parties must give their
  consent freely.


This was reiterated at the Council of Trent but dates from much earlier:


  The statement of Pope Nicholas I in which he declared in 866, "If the
  consent be lacking in a marriage, all other celebrations, even should
  the union be consummated, are rendered void", shows the importance of
  a couple's consent to marriage. It has remained an important part of
  church teaching through the years.


You can read an extended dance remix of all this in the Summa Theologica.

For this reason forced marriage is largely constrained to parts of Asia, Africa, and the Middle East that have not had enough Christian influence to affect their laws. So yes, it is a cultural issue, but one that the Christian Church usually strives to influence, and has done so successfully in many cases.