Are Christians supposed to be like-minded? Brotherly love is a commandment: 1 John 4:20,21 …and this commandment have we from him, That he who loveth God love his brother also.

Brotherly love is a Christian trademark: John 13:35 By this shall all [men] know that ye are my disciples, if ye have love one to another.

The early church coexisted predominantly in harmony while under great threat of physical harm: Throughout the book of Acts (1:14; 2:1; 2:46; 4:24; 5:12; 7:57; 8:6; 12:20; 15:25; 18:12; 19:29) the early Church is said to be in “one accord”.  Paul in Romans 15:6 admonishes his followers: “That ye may with one mind [and] one mouth glorify God, even the Father of our Lord Jesus Christ”. 

There was a oneness of “Spirit”: 1Corinthians 12:13 For by one Spirit are we all baptized into one body, whether [we be] Jews or Gentiles, whether [we be] bond or free; and have been all made to drink into one Spirit.  Also see: (1Corinthians 4:12; Ephesians 2:8; Ephesians 4:4; Philippians 2:2)

Today there are some 41,000 Christian Denominations in the World according to: http://christianity.about.com/od/denominations/p/christiantoday.htm.

Has their ever been any significant historical movements within Christianity to reverse the splintering?

Modern Christians seem to accept that a oneness of Spirit is an impossibility, are there any current movements within Christianity towards reconciliation and a common accord?

Most Christians await the return of Jesus Christ, are there any denominations that are concerned about His reaction to what He finds?
It is obviously the will of Jesus Christ, the builder of the Church, that Christians should live in one accord. However, if we can belief that everything is controlled and monitored by God, then I do not think we should take our present splintering situation negatively. This might be the will of God, who knows?
There are some reasons why new denominations are born.

The mother church goes off the right track.
Disagreement in political or management inside the church.
Commotion among the members.
Disagreement in specific doctrines.
etc.

When the mother church is clearly in the wrong and is not in a position to repent, there is no choice but to form a new group. Sometimes, political disagreement is the will of God to extend His kingdom as in the case of Paul and Barnabas, who splitted party which in fact was God's plan to reach out to Gentiles in Macedonia, for a greater ministry. It is also the work of Satan to divide the church by stirring the members to fight among themselves. Disagreement in doctrine is a serious issue where the power of Satan is usually at work. Satan brings confusion and doubt to the truth.
There is no doubt that some denominations are planted by the Devil as we see in  the parable of the Weeds. But God allow the true and false church to grow together.

Matthew 13:30 Let both grow together until the harvest. At that time I will tell
the harvesters: First collect the weeds and tie them in bundles to be
burned; then gather the wheat and bring it into my barn.’”

Everything is in God's hand. We must trust in Him.
There are some preachers who try bring denominations together and deliver good sermons towards unity in Christianity. Also, these days we have many non-denominational christians, who takes less interest in denominations but focus more on ministry and unification.
Actually, we are not that different from each other. Each of us are but a single organ in the Body of Christ and Christ is the Head of us all.